WAEC 2019 · Paper 2 · Q3

(a)
Find the equation of the circle centre $(2, 3)$ which passes through the $y$ -intercept of the line $3x - 2y + 6 = 0$ .
Show the answer
$x^2 + y^2 - 4x - 6y + 9 = 0$

Worked solution (try it first)

The $y$ -intercept is where $x = 0$ : $-2y + 6 = 0$ , so $y = 3$ : the point $(0, 3)$ .
$r^2 = (0 - 2)^2 + (3 - 3)^2 = 4$ .
$(x - 2)^2 + (y - 3)^2 = 4$ .
Expand: $x^2 - 4x + 4 + y^2 - 6y + 9 = 4$ , so $x^2 + y^2 - 4x - 6y + 9 = 0$ .