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.