WAEC Further Mathematics 2012 Paper

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

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

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

Comparing with the given equation: $3x^{2} + 3y^{2} + 24x - 12y = 15$

Making the coefficients of $x^{2}$ and $y^{2}$ = 1, we have

$x^{2} + y^{2} + 8x - 4y = 5$

$2a = -8 \implies a = -4$

$2b = 4 \implies b = 2$

$r^{2} - a^{2} - b^{2} = 5 \implies r^{2} = 5 + (-4)^{2} + (2)^{2} = 5 + 16 + 4 = 25$

$\therefore r = 5$