Question

A circle has a diameter with endpoints (-8, 2) and (-2, 6). What is the equation of the circle? r2 = (x - 3)2 + (y + 4)2 r2 = (x - 5)2 + (y + 4)2 r2 = (x + 5)2 + (y - 4)2 r2 = (x + 3)2 + (y - 4)2

Answer 1

Hello : here is a solution : 

Answer 2

`r^(2)=(x+5)^(2)+(y-4)^(2)`

Explanation:

we know that

The 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

r is the radius of the circle

Step 1

we have

`A(-8,2)\\B(-2,6)`

Find the center of the circle

The center of the circle is the midpoint between point A and point B

The formula to calculate the midpoint is equal to

`M((x1+x2)/(2) ,(y1+y2)/(2) )`

substitute the values

`M((-8-2)/(2) ,(2+6)/(2))`

`M({-5 ,4)`

the equation of the circle is equal to

`(x+5)^(2)+(y-4)^(2)=r^(2)`