WAEC 2018 · Paper 2 · Q4

Coordinate geometry & circles

The radius of the circle $x^2 + y^2 - 4x - 2y + C = 0$ is $3\sqrt2$ . Find the:

(a)
value of $C$ ;
(b)
equation of the diameter through $(9, 2)$ .
Show the answer
$7y - x - 5 = 0$

Worked solution (try it first)

(a)

$2g = -4$ and $2f = -2$ , so the centre is $(2, 1)$ .
$r^2 = g^2 + f^2 - C$ : $18 = 4 + 1 - C$ , so $C = -13$ .

(b)

A diameter passes through the centre $(2, 1)$ .
Through $(2, 1)$ and $(9, 2)$ : gradient $\frac{1}{7}$ , so $y - 1 = \frac17(x - 2)$ .
$7y - 7 = x - 2$ , so $7y - x - 5 = 0$ .

Report a problem with this question