Finding an equation for a circle

Question

PQ is a diameter of a circle. find an equation for the circle when p is (0,5) and when q is (0,-1)

Answer 1

P(0,5) Q(0,-1)

PQ is a diameter of circle, so midpoint of PQ is center of circle.

Mid point of PQ = (0,2)

PQ = √[(0-0)^2+(-1-5)^2]

= √36

= 6

Diameter is 6, then radius would be 3.

Radius of circle is 3.

Circle equation is (x-h)^2+(y-k)^2 = r^2

(x-0)^2+(y-2)^2 = 3^2

x^2+y^2+4-4x = 9

Subtract 9 from each side.

Required circle equation is x^2+y^2-4x-5 =0.