Answer: The equation of a circle can be written in the form (x−h)2+(y−k)2=r2, where (h,k) is the center of the circle and r is its radius.
The center of the circle is the midpoint of the diameter. The midpoint of the line segment with endpoints (−8,2) and (−2,6) can be found using the midpoint formula:
(2−8+(−2),22+6)=(−5,4)
So the center of the circle is (−5,4).
The radius of the circle is half the length of the diameter. The length of the diameter can be found using the distance formula:
((−2)−(−8))2+(6−2)2=36+16=52
So the radius of the circle is 52/2.
Substituting these values into the equation for a circle gives us:
(x+5)2+(y−4)2=(252)2
Simplifying this equation gives us:
(x+5)2+(y−4)2=13
So the equation of the circle with diameter endpoints (−8,2) and (−2,6) is (x+5)2+(y−4)2=13.
Explanation: