IIT JEE Advanced 2008 Paper 1

We have
(ax2+by2+c)(x2–5xy+6y2) = 0
⇒ x2−5xy+6y2 = 0
(x - 2y) (x - 3y) = 0
⇒ x - 2y = 0 or x - 3y = 0 , represents two straight lines.
Now , ax2+by2+c = 0
Let a = b. Then
x2+y2 = (−

c

a

)
Here, if a and c are of opposite sign, then the equation represents a circle.