find the equation of a circle whose diameter has ends points A=(-4, 3)and B=(5, 7)and it subtends a 90 degree at the circumference.

Answer 1

the centre must be the midpoint of A and B and that midpoint is (1/2 , 5)
so the equation must be:
(x - 1/2)^2 + (y - 5)^2 = r^2
but (5,7) lies on it, so
(5-1/2)^2 + (7-5)^2 = r^2
81/4 + 4 = r^2
r^2 = 97/4

(x - 1/2)^2 + (y - 5)^2 = 97/4

btw, the fact that a diameter subtends a 90° is true for all circles, so it was redundant information