Question

Find the equation of the circle which passes through (3, −2), (−2, 0) and has its centre on the line 2x − y = 3.

Answer 1

Let the required equation of the circle be $x^2+y^2+2gx+2fy+c=0$. ...(1)
It is given that the circle passes through (3, −2), (−2, 0).
∴ $13+6g-4f+c=0$ ...(2)
$4-4g+c=0$ ...(3)

The centre lies on the line 2x − y = 3.
∴ $-2g+f-3=0$ ...(4)

Solving (2), (3) and (4):

$g=\frac{3}{2},f=6,c=2$

Hence, the required equation of circle is $x^2+y^2+3x+12y+2=0$.