Question

A circle is entered on the point (-1,5) and contains the point (7,11). What is the area of this circle?

Answer 1

100π units square

Explanation:

The circle is centered on the point (-1,5) and contains the point (7,11).

We can find the radius, using the distance formula,

`r=√((x_2-x_1)^2+(y_2-y_1)^2)`

We substitute the points to get:

`r=√((7- - 1)^2+(11- 5)^2)`

This implies that:

`r=√((8)^2+(6)^2)`

`r=√(64+36)`

`r = √(100)`

`r = 10 \: units`

The area of a circle is given by:

`A=\pi \: {r}^(2)`

Plug in the radius into the formula to get:

`A=\pi * {10}^(2)`

`A=\pi * 100`

`A=100\pi`

The area is 100π square units or 314 square units