Question

Find the equation of the circle which passes through the points (20, 3), (19, 8) and (2, –9). Find its centre and radius.

Answer 1

By substitution of coordinates in the general equation of the circle given by x² + y² + 2gx + 2fy + c = 0

We have 40g + 6f + c = – 409

38g + 16f + c = – 425

4g – 18f + c = – 85

From these three equations, we get

g = – 7

f = – 3

And c = –111

Hence, the equation of the circle is

x² + y² – 14x – 6y – 111 = 0

or (x – 7)² + (y – 3)² = 13²

Therefore, the centre of the circle is (7, 3) and radius is 13.