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

Answer:

$r^{2}=(x+5)^{2}+(y-4)^{2}$

Step-by-step 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

$M(\frac{x1+x2}{2} ,\frac{y1+y2}{2} )$

substitute the values

$M(\frac{-8-2}{2} ,\frac{2+6}{2})$

$M({-5 ,4)$

the equation of the circle is equal to

$(x+5)^{2}+(y-4)^{2}=r^{2}$