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Straight Lines and Pair of Straight Lines question

2008 · Shift 1 · Q43

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JEE Advanced
Mathematics
Straight Lines and Pair of Straight Lines
2008 · Shift 1 · Q43

Straight Lines and Pair of Straight Lines question

2008 · Shift 1 · Q43

JEE AdvancedMathematicsStraight Lines and Pair of Straight LinesMCQ+3 / −1

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

(a{x^2} + b{y^2} + c)({x^2} - 5xy + 6{y^2}) = 0

represents :

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

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