Question

Find an equation of the circle whose diameter has endpoints (-5-4) and (3-6)

Answer 1

d = √((-5 - 3)² + (-4 - 6)²) = √((-8)² + (-10)²)

= √(64 + 100) = √164 = 2√41

r = √41, so r² = 41

Center = ((-5 + 3)/2, (-4 + (-6))/2)

= (-2/2, -10/2)

= (-1, -5)

So the equation of this circle is

(x + 1)² + (y + 5)² = 41