The equation x^2 + 4xy + y^2 + 2x + 4y + 2 = 0 represents - Vidyadip

MCQ

The equation ${x^2} + 4xy + {y^2} + 2x + 4y + 2 = 0$ represents

A
An ellipse
B
A pair of straight lines
✓
A hyperbola
D
None of these

✓

Answer

Correct option: C.

A hyperbola

c
(c) Obviously ${h^2} > ab$ and

$\Delta = (1)\,(1)\,(2) + 2(2)\,(1)\,(2) - (1)\,{(2)^2} - (1)\,{(1)^2} - 2{(2)^2} < 0$

Hence it is a hyperbola.

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