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

MHT CET 2022 Mathematics question

Let a and b two non-zero real numbers The equation represents

(A)four straight lines, when c = 0 and a, b of the same sign
(B)a circle and an ellipse when a and b are of the same sign and c is of sign opposite to that of a
(C)two straight lines and a hyperbola when a and b are of the same sign c is of sign opposite to that of a
(D)two straight lines and a circle, when a = b and c is of sign opposite to that of aCorrect

Answer: (D)

Solution

The equation is a product of two factors set to zero, so it represents the union of the curves and . The first factors as , which is a pair of straight lines. For the second, if and c has sign opposite to a, then is a circle. So the whole

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Question ID VK-094307