WAEC Further Mathematics 2013 Paper

The equation of a circle is given as $(x - a)^{2} + (y - b)^{2} = r^{2}$.

Expanding, we have: $x^{2} - 2ax + a^{2} + y^{2} - 2by + b^{2} = r^{2}$

$x^{2} + y^{2} - 2ax - 2by + a^{2} + b^{2} = r^{2}$

Comparing with the equation, $x^{2} + y^{2} - 8x + 9y = -15$, we have

$2a = 8; 2b = -9; r^{2} - a^{2} - b^{2} = -15$

$a = 4; b = \frac{-9}{2}$

$\therefore r^{2} = -15 + 4^{2} + \left(\frac{-9}{2}\right)^{2}$

= $-15 + 16 + \frac{81}{4} = \frac{85}{4}$

$r = \sqrt{\frac{85}{4}} = \frac{1}{2}\sqrt{85}$