Let a and b be non-zero and real numbers. Then, the equation (ax^2+by^2+c ) (x^2-5xy+6y^2 )=0 represents

JEE Main Mathematics question

Let and be non-zero and real numbers. Then, the equation represents

(A)Four straight lines, when and are of the same sign
(B)Two straight lines and a circle, when and is of sign opposite to that of Correct
(C)Two straight lines and hyperbola, when and are of the same sign and is of sign opposite to that of
(D)A circle and an ellipse, when and are of the same sign and is of sign opposite to that of

Answer: (B)

Solution

always gives two straight lines. The factor is a real circle when and has the sign opposite to ; for and of the same sign it is only the origin (so (A) fails), and

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Question ID VK-024318