Question

Find an equation of the circle whose diameter has endpoints (-1, -2) and (5,
6).

Answer 1

(x - 2)^2 + (y - 2)^2 = 25.

Explanation:

The diameter of the circle is √(5 - -1)^2 +(6 - -2)^2

= √(36 + 64)

= √100

= 10

So the radius is 10/2 = 5.

The centre of the circle is the midpoint of the diameter

= (-1+5)/2 , -2+6)/2

= (2, 2).

So the equation of the circle is

(x - a)^2 + (y - b)^2 = r^2 where r = radius and (a, b) is the centre is:

(x - 2)^2 + (y - 2)^2 = 25