Question

Find the center and radius of the following circles.

1. x² + y² – 4x – 8y – 45 = 0

2. x² + y² – 8x – 10y - 22 = 0

3. 2x² + 2y² – x = 0

Answer 1

1. Comparing with the general equation we have

g = -2; f = -4; c = -45

Centre – (-g, -f) ⇒ (2, 4)

Radius – \(\sqrt{g^2 + f^2 - c}\)

= \(\sqrt{4+16+45} = \sqrt{65}\)

2. Comparing with the general equation we have

g = -4; f = -5; c = -22

Centre – (-g, -f) ⇒ (4, 5)

 Radius – \(\sqrt{g^2 + f^2 - c}\)

= \(\sqrt{4+16+45} = \sqrt{65}\)

3. Convert the equation into standard form