Question

If the endpoints of the diameter of a circle are (−8, −6) and (−4, −14), what is the standard form equation of the circle?

Answer 1

Answer: (x + 6)2 + (y + 10)2 = 20

Answer 2

The standard form of a circle is (x-h)+(y-k)^2=r^2

h and k represent the center of the circle and to find the center you have to find the midpoint of the two endpoints.
the midpoint formula states to find the average of the x values and the y values (to find the average you add the terms together and divide by however many you have.. In this case add the two x/y terms and divide by 2).

the midpoint is (-6,-10) which means that the standard form would be 
(x+6)^2+(y+10)^2=r^2

but you still have to find the measure of r, the radius. So you'd use the distance formula to find the diameter and divide by 2 to find the radius.
distance formula is d=√(x-x)²+(y-y)²
so the diameter is 4√5, divide by 2 and the radius is 2√5