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

JEE Advanced 2008 Mathematics question

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

+ + - 5xy + = 0

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 a 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)

The second factor always gives two lines , . Checking each case for the

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Question ID VK-000765