JAMB 1999 · UME · Q26

Find a positive value of $a$ if the centre of the circle $x^2 + y^2 - 2ax + 4y - a = 0$ is $(a, -2)$ and the radius is 4 units.

Worked solution (try it first)

Compare with $x^2 + y^2 + 2gx + 2fy + c = 0$ : here $g = -a$ , $f = 2$ and $c = -a$ .
The radius satisfies $r^2 = g^2 + f^2 - c$ , so $16 = a^2 + 4 + a$ .
Rearrange: $a^2 + a - 12 = 0$ , which factorises as $(a + 4)(a - 3) = 0$ .
The positive value is $a = 3$ , option C.