Find the equation of the circle that has a diameter with endpoints (-4,8) and (4,-4)

Answers

Answer 1

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First we need to find the distance between two points which is the diameter of the circle .

_________________________________

Suppose :

a = ( - 4 , 8 )

b = ( 4 , - 4 )

We have following equation to find the distance between two points.

[tex]distance = diameter = d[/tex]

[tex]d = \sqrt{ ( \: {y(b) - y(a)} \: )^{2} + ( \: {x(b) - x(a)} \: )^{2} } \\ [/tex]

Now just need to put the coordinates :

[tex]d = \sqrt{ ({ - 4 - 8})^{2} + ( \: {4 - ( - 4)} \: )^{2} } \\ [/tex]

[tex]d = \sqrt{ ({ - 12})^{2} + ({4 + 4})^{2} } [/tex]

[tex]d = \sqrt{ ({ - 12})^{2} + ({8})^{2} } [/tex]

[tex]d = \sqrt{144 + 64} [/tex]

[tex]d = \sqrt{208} [/tex]

[tex]d = \sqrt{4 \times 52} [/tex]

[tex]d = \sqrt{4 \times 4 \times 13} [/tex]

[tex]d = \sqrt{ {4}^{2} \times 13 } [/tex]

[tex]d = 4 \sqrt{13} [/tex]

This is the diameter of the circle.

We know that :

[tex]diameter = 2 \times radius[/tex]

So :

[tex]4 \sqrt{13} = 2 \times radius[/tex]

Divide sides by 2

[tex] \frac{4 \sqrt{13} }{2} = \frac{2 \times radius}{2} \\ [/tex]

[tex]2 \sqrt{13} = radius[/tex]

Remember it.

_________________________________

To find the equation of the circle except the radius , we need the coordinates of the centre.

The midpoint of the diameter is the centre of the circle .

So we have to find the midpoint of the diameter .

Look :

[tex]midpoint = center = o[/tex]

[tex]o = ( \: \frac{x(a) + x(b)}{2} \: , \: \frac{y(a) + y(b)}{2} \: ) \\ [/tex]

[tex]o = ( \: \frac{ - 4 + 4}{2} \: , \: \frac{8 - 4}{2} ) \\ [/tex]

[tex]o = ( \: \frac{0}{2} \: , \: \frac{4}{2} \: ) \\ [/tex]

[tex]o = ( \: 0 \: , \: 2 \: )[/tex]

This the coordinates of the centre.

_________________________________

Equation of the circle has a form like this :

[tex]( {x - m})^{2} + ({y - n})^{2} = {r}^{2} [/tex]

In which :

[tex]m = x - coordinate \: \: of \: \: the \: \: center \\ [/tex]

[tex]n = y - coordinate \: \: of \: \: the \: \: center \\ [/tex]

[tex]r = radius[/tex]

_________________________________

[tex]o = ( \: 0 \: , \: 2 \: )[/tex]

[tex]radius = 2 \sqrt{13} [/tex]

Thus :

[tex] ({x - 0})^{2} + ({y - 2})^{2} = ({2 \sqrt{13} })^{2} \\ [/tex]

[tex] {x}^{2} + ({y - 2})^{2} = 4 \times 13[/tex]

[tex] {x}^{2} + ({y - 2})^{2} = 52 [/tex]

This is the equation of the circle .

And we're done....

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Related Questions

Explain how to plot the point (3, –7) on the coordinate plane.


PLS HELP FAST

P.S. i only need one small pharagraph

Answers

We have the values 3 and -7. The first number is x and the second is y. Meaning, x (the first number) would go on the x axis while y (the second number) will go on the y axis. We will plot x on 3 and since y is negative we will plot it further more down to -7.

Answer:

First you go to the x-axis put your point on where the coordinate says. In this case, 3. Then go to the y-axis and put your coordinate there, -7. The x-axis is first also knows as the first number in the coordinate.

Step-by-step explanation:

E23 I put as answer was correct :)

Find the measure of each numbered angle.

Answers

Answer:

∠3 = 22°

∠4 = 22°

∠5 = 88°

Step-by-step explanation:

86 + 72 = 158

180 - 158 = 22

∠3 ≅∠4 they're verticle angles

22+ 70 = 92

180 - 92 = 88

Sorry really need points

Troy has to order 8 pounds of ham,15 pounds of cheese, and 12 pounds of turkey. What is the total cost of Troy‘a order?

Answers

Total cost is $93.75

Answer:

The answer is $93.75

Step-by-step explanation:

Doctors nationally believe that 74% of a certain type of operation are successful. In a particular hospital, 57 of these operations were observed and 47 of then were successful. At alpha is equal to 0.05, is this hospital's success rate different from the national average

Answers

Thanks for the points
You deserve a real answer
Ask your teacher

Jaclyn and Henry secured a $225,000 mortgage at 5% annual interest for 20 years. This results in a monthly payment of $1484.90 and the interest paid in month one is $937.50. Assume they only make the minimum payment each month. How much is the balance reduced in month one? What is the beginning balance for month two?

Answers

The answers for the 1st part is 547.40 and the answer for the 2nd part is 224,452.60

Re-write the quadratic function below in Standard Form
y = -(x – 3)2 +8

Answers

Answer:

y = -x² + 6x - 1

General Formulas and Concepts:

Algebra I

Standard Form: ax² + bx + c = 0Expanding by FOIL (First Inside Outside Last)Combining like terms

Step-by-step explanation:

Step 1: Define equation

y = -(x - 3)² + 8

Step 2: Rewrite

Expand [FOIL]:                    y = -(x² - 6x + 9) + 8Distribute -1:                        y = -x² + 6x - 9 + 8Combine like terms:           y = -x² + 6x - 1

Which of the following is a factor of 7x2 - 12x - 4? (6 points)
O 7x - 2
O x + 2
Ox-4
O None of the above

Answers

Answer:

We conclude that 'None of the above' is the correct answer.                    

Step-by-step explanation:

Given the expression

[tex]7x^2\:-\:12x\:-\:4[/tex]

Breaking the expression into groups

[tex]7x^2\:-\:12x\:-\:4=\left(7x^2+2x\right)+\left(-14x-4\right)[/tex]

Factor out [tex]x[/tex] from [tex]7x^2\:+\:2x[/tex]

[tex]=x\left(7x+2\right)[/tex]

Factor out -2 from [tex]\left(-14x-4\right)[/tex]

[tex]=-2\left(7x+2\right)[/tex]

so the expression becomes

[tex]7x^2\:-\:12x\:-\:4=\left(7x^2+2x\right)+\left(-14x-4\right)[/tex]

                         [tex]=x\left(7x+2\right)-2\left(7x+2\right)[/tex]

Factor out the common term [tex]7x+2[/tex]

                         [tex]=\left(7x+2\right)\left(x-2\right)[/tex]

Therefore, from the given options, we conclude that 'None of the above' is the correct answer.                    

The center of a circle and a point on the circle are given. Write the equation of the circle in standard form.
center: (2,-5), point on the circle: (-4,-5)

Answers

Answer:

25= (x-2)² + (y+4)²

Hope this helps!!!

Answer:

[tex](x-2)^2+(y+5)^2=36[/tex]

Step-by-step explanation:

The standard form of a circle is given by the equation:

[tex](x-h)^2+(y-k)^2=r^2[/tex]

Where (h, k) is the center and r is the radius.

We know that the center is (2, -5). So, we can substitute 2 for h and -5 for k. This yields:

[tex](x-(2))^2+(y-(-5))^2=r^2[/tex]

Simplify:

[tex](x-2)^2+(y+5)^2=r^2[/tex]

Now, we need to determine r. We know that a point on the circle is (-4, -5). Thus, we can determine r by substituting -4 for x and -5 for y. This yields:

[tex](-4-2)^2+(-5+5)^2=r^2[/tex]

Evaluate:

[tex](-6)^2+(0)^2=r^2[/tex]

Evaluate:

[tex]36=r^2[/tex]

Hence, the radius squared is 36.

We do not actually need to solve for r, as we will square it anyways.

We will substitute 36 for r squared. Hence, our equation is:

[tex](x-2)^2+(y+5)^2=36[/tex]

The radius will thus be 6 units.

Which statements are TRUE? Select all that apply.

A. Marisa drives 112 miles in 1 hour and 45 minutes, which means her speed is 64 miles per hour.
B. If 6 pens cost $7.74, then 7 pens cost $9.03.
C. If Raymond drives at a speed of 57 miles per hour, then it takes him 4 hours and 10 minutes to drive 256.5 miles.
D. If 17 identical cans of soup cost $38.59, then 3 of the cans must cost $6.81.
E. Mr. Mayes buys two dozen eggs for $8.40, which means that he pays 70 cents per egg.

Answers

Answer:

A, B, D are true

Step-by-step explanation:

A)  Speed = Distance travelled ÷ time taken

                 = 112 ÷ 1.75

                  = 64 miles per hour

True

B) Cost of 6 pens = $7.74

   Cost of 1 pen    = 7.74 ÷ 6 = $ 1.29

   Cost of 7 pens = 1.29 * 7   = $ 9.03

TRUE

C) Speed = 57 miles per hour

4 hour 10 minutes = 250 minutes

Distance traveled in an hour  = 57

Distance traveled in 250 minutes = (57* 250)   ÷ 60 = 237.50 miles

FALSE

D) Cost of 17 cans = $ 38.59

   Cost of 1 can      = 38.59 ÷ 17 = $2.27

   Cost of 3 cans    = 2.27 * 3 = $ 6.81

TRUE

e) Cost of two dozen eggs = $ 8.40

    Cost of an egg                = 8.40 ÷  24  =   $ 0.35

FALSE

what is the equation in point slope form of a line that passes through the points (-4,-1)and5,7)

Answers

Answer:

[tex]\frac{8}{9}[/tex]

Step-by-step explanation:

using the image attached as reference

(-4,-1) - the -4 becomes x1, and the -1 becomes y1

(5,7)  - the 5 becomes x 2 and the 7 becomes y2

plug this information into the equation

      7-(-1)

m=----------      

      5-(-4)

solve

       8

m=----------    

        9

​so your slope would become 8/9

124.44 is 34 percent of what number?​

Answers

Answer:

out of 100

Step-by-step explanation:

Please see question below.
What is 112% of 50?
2
Your answer
Please see question below.

Answers

Answer: 56

Step-by-step explanation:

Answer:

112% of 50 is 56

Step-by-step explanation:

100% of 50 is 50.

We have to find 12% of 50, and then add it to 50 to get 112% of 50.

12% of 50 is the same as .12 x 50 which is 6.

50 + 6 = 56

I Hope That This Helps! :)

If f(x) = (2x^3 − 4)^6, then what is f '(x)?

21x^2(x^3 − 4)^5
21x^8
6(2x^3 − 4)^5
6(2x^3 − 4)^5(6x^2)

Answers

The correct answer is:

6(2x^3-4)^5(6x^2)

Explanation:

That is the derivative after you differentiate using the Chain Rule.

If sin∠X = cos∠Y and m∠X = 72°, what is the measure of ∠Y?
a. 18°
b. 72°
c. 90°
d. 108°

Answers

Answer:

A. 18°

Step-by-step explanation:

Using the cofunction identity

sin x = cos(90 - x)

Hence

sin72° = cos(90 - 72)° = cos18° ⇒ ∠Y = 18°

Answer:

The answer is 18.

Step-by-step explanation:

90-72=18

Which statements are true of all squares? Select three options.

The diagonals are perpendicular.
The diagonals are congruent to each other.
The diagonals bisect the vertex angles.
The diagonals are congruent to the sides of the square.
The diagonals are twice the length of one side of the square.

Answers

Answer:

The diagonals are perpendicular.

The diagonals are congruent to each other.

The diagonals bisect the vertex angles.

The statements that are true of squares include:

The diagonals are perpendicular.The diagonals are congruent to each other.The diagonals bisect the vertex angles.

What's a square?

It should be noted that a square simply means a shape that has four sides equal. The angles are also 360° since they're 90° each.

In squares, the diagonals are perpendicular and the diagonals are congruent to each other.

Learn more about square on:

https://brainly.com/question/12831058

Acidity is measured on the pH scale. The acidity of a substance is given by pH=−logH, where H is the concentration of Hydrogen ions. If a substance has an H value of 0.00032, which shows a valid step in the process of calculating the pH of the substance?a. pH = - log 0.0032.b. - log(3.2.10-4)= pH.c. log(3.2.10-4)= pH.d. log(3.2.10*) = -pH.e. pH = log 0.00032.

Answers

Answer:

-log(3.2•10^-4)=pH

Step-by-step explanation:

The choice which shows a valid step in the process of calculating the pH of the substance is; Choice B. - log(3.2.10-⁴) = pH.

According to the question;

The acidity of a substance is given by pH=−logH, where H is the concentration of Hydrogen ions.

Therefore, when H = 0.00032

pH = - log 0.00032

However; 0.00032 can be written in standard form as; 3.2.10-⁴

Therefore, Choice B is correct.

Read more:

https://brainly.com/question/17093969

20 POINTS!!!
The volume of a ball is 30 cm^3. If the diameter of the ball is dilated by a scale factor of 5, what is the new volume of the ball? Don't include the units

Answers

girl you lied it was only 10 points try again

I will give u 50 points and brainlest pls help

Answers

Answer:

The bicyclist rides 72 miles in 4 hours

Step-by-step explanation:

The vertical axis represents the number of miles while the horizontal axis is the duration. The intersecting point is the time and distance taken hence 72 miles in 4 hours.

Answer:

if you know this or not but 5  points is not 50

Step-by-step explanation:

71 2/3 as a fraction

Answers

Answer:

215/3

Step-by-step explanation:

71 multiplied by 3 (denominator) + 2 (remainder) divided by 3

The improper fraction for the given mixed fraction is 215/2.

The given fraction is [tex]71\frac{2}{3}[/tex].

These are just improper fractions written as a sum of whole number and a proper fraction. (improper fraction has the upper value(also called numerator) bigger or equal to denominator(the bottom value) and proper fraction has numerator value is less than that of the denominator)

They are written and can be converted to fraction as: [tex]a\frac{b}{c} = \frac{(a\times c)+b}{c}[/tex]

Now, [tex]71\frac{2}{3}=\frac{71\times3+2}{3}[/tex]

= (213+2)/3

= 215/3

Therefore, the improper fraction for the given mixed fraction is 215/2.

Learn more about mixed fractions here:

brainly.com/question/886123.

#SPJ6

cv6gv uig. ih 8h 88h oh 9h​

Answers

Answer:

what

Step-by-step explanation:

Answer:

HAVE A FANTASTIC DAY!!!XD

Step-by-step explanation:

BRAINLIEST WOULD BE MUCH APPRECIATED!!!

Nora is 4 years older than Hina . If the sum of their ages is at most 45 years ,find the maximum possible age of Hina. *

b) 25 years

a) 20 years

c) 15 years

choose the correct answer

Answers

Answer:

a) 20 years

Step-by-step explanation:

Hina:  x

Nora:  x + 4

x + x + 4 ≤ 45

2x + 4 ≤ 45

2x ≤ 41

x ≤ 20.5

20 years old and 15 years old would be ≤ 20.5 but the question asked for maximum possible age so 20 years old it is.

A waterfall has a height of 1200 feet. A pebble is thrown upward from the top of the falls with an initial velocity of 24 feet per second. The​ height, h, of the pebble after t seconds is given by the equation -16t^2+24t+1200 . How long after the pebble is thrown will it hit the​ ground?

Answers

Answer: 9.44 seconds

Step-by-step explanation:

A movement equation in the vertical axis is usually written as follows:

p(t) = (-g/2)*t^2 + v0*t + p0

where:

g is the gravitational acceleration, in this case is 32 ft/s^2, then -g/2 = -16ft/s^2

v0 is the initial velocity, in this case, 24 ft/s

p0 is the initial height, in this case, 1200ft

Then, when p(t)  = 0ft will mean that the pebble will hit the ground, then we need to calculate:

p(t) = -16t^2+24t+1200  = 0

and find the value of t, this is a quadratic equation, then we can use the Bhaskara equation to find the two solutions, these are:

[tex]t = \frac{-24 +- \sqrt{24^2 - 4*(-16)*1200} }{2*-16} = \frac{-24 +- 278.2}{-32}[/tex]

Then the two solutions are:

t = (-24  + 278.2)/-32 = -7.94 seconds (we can discard this one, because the negative time is not really defined)

t = (-24 - 278.2)/-32 = 9.44 seconds

Then the pebble needs 9.44 seconds to hit the ground

If you have 3 cups of pineapple juice, how many total cups of lunch can you make?

Answers

About 6 that’s what I came up with

what is the solution to this equation?
x-4=17
A. x=13
B. x=11
C. x=23
D. x=21​

Answers

Answer:

d. x=21

Step-by-step explanation:

x-4=17

x-4 +4=17+4

x=21

A board measures 15 meters in length and is cut into two pieces. One-piece measures 7 meters. Write an equation to find the length of the other piece?

Answers

Answer:

15 = 7 + m

Step-by-step explanation:

If 15 is the total then it goes on the other side of the equal sign. You have one side so if you add it to the missing side it should equal 15.

what is the average rate of change of f(x)= –8x+20 over the interval [–17,–10].

Answers

Answer:

Mein Name ist, mein Name ist, ich bin der beste Rapper, den es gibt

Step-by-step explanation:

What is the answer to 32divided by 7/8

Answers

Answer:

Boyy

Step-by-step explanation:

Find the new amount.

15 liters increased by 60% is
( ? ) liters.

Answers

Answer:

24

Step-by-step explanation:

15*1.60=24

Two parallel lines are cut by a transversal. Angle 1 measures (4x + 28)°, and the angle adjacent to the alternate exterior angle with angle 1 measures (14x + 8)°. What is the value of x? One-half 2 8 12

Answers

Answer:

8

Step-by-step explanation:

Its right on edge

Answer:8

Step-by-step explanation:

Which expression means 25% off an originally prices item?
a. 1.25p
b. P - 0.25p
c. 0.25p
d. P + 0.75p

Answers

Answer:

b.

Step-by-step explanation:

dfghjkldesrycfhgyhkjludawregdyhukhu

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