Question

Which equation represents a circle that contains the point (-2,8) and has a center at (4,0)?

Distance Formula: (x2-x1)^2 + (y2-y1)^2

(Answer Choises In Photo)

Answer 1

It’s A

Explanation:

Answer 2

The equation of the circle is
`(x-4)^(2)+(y)^(2) =100`

Explanation:

we know that

The general equation of the circle into center-radius form is equal to

`(x-h)^(2)+(y-k)^(2) =r^(2)`

where

(h,k) is the center of the circle

In this problem

`(h,k)=(4,0)`

substitute

`(x-4)^(2)+(y-0)^(2) =r^(2)`

`(x-4)^(2)+(y)^(2) =r^(2)`

Find the radius

we know that

The distance between the points (-2,8) and (4,0) is equal to the radius

Applying the distance 's formula

`d=\sqrt{(0-8)^(2)+(4+2)^(2)}`

`d=\sqrt{100`

`d=10\ units`

so

the radius is equal to
`r=10\ units`

substitute

`(x-4)^(2)+(y)^(2) =10^(2)`

`(x-4)^(2)+(y)^(2) =100`