8. Find the area of a circle with center
(2, 3) that passes through (2,7)
Use 3.14 for a
F 12.58 units H 41.38 units?
6 25.12 units? J 50.24 units
Pls help

Answer:

Area of circle = 50.24 units

Option J is correct answer.

Step-by-step explanation:

We need to find the area of a circle with centre  (2, 3) that passes through (2,7)

The formula used to find area of circle is:

[tex]Area\: of\: circle=\pi \:r^2[/tex]

We need to find radius.

The radius can be found using the distance between points (2,3) and (2,7)

The The distance formula is: [tex]Distance = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Putting values and finding length

We have: [tex]x_1=2, y_1=3, x_2=2, y_2=7[/tex]

Putting values and finding distance

[tex]Distance = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\Distance = \sqrt{(2-2)^2+(7-3)^2}\\Distance = \sqrt{(0)^2+(4)^2}\\Distance = \sqrt{0+16}\\Distance = \sqrt{16}\\Distance = 4[/tex]

So, we found Distance = 4

Therefore, the radius of circle is 4

Now, finding area:

[tex]Area\: of\: circle=\pi \:r^2\\Area\: of\: circle=3.14\times (4) ^2\\Area\: of\: circle=3.14\times 16\\Area\: of\: circle=50.24 \:units[/tex]

So, Area of circle = 50.24 units

Option J is correct answer.

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