Question

8. Find the area of a circle with center

Answer 1

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:

$Area\: of\: circle=\pi \:r^2$

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: $Distance = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Putting values and finding length

We have: $x_1=2, y_1=3, x_2=2, y_2=7$

Putting values and finding distance

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

So, we found Distance = 4

Therefore, the radius of circle is 4

Now, finding area:

$Area\: of\: circle=\pi \:r^2\\Area\: of\: circle=3.14\times (4) ^2\\Area\: of\: circle=3.14\times 16\\Area\: of\: circle=50.24 \:units$

So, Area of circle = 50.24 units

Option J is correct answer.