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

JEE Advanced Mathematics question

Let be non-zero real numbers. 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

Answer: (B)

: the two lines , . The other factor is .

- (a) , same sign: is only the point , not two lines. ✗ - (b) ,

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Question ID VK-110678