The equation x^2 - 2xy + y^2 + 3x + 2 = 0 represents - Vidyadip

MCQ

The equation ${x^2} - 2xy + {y^2} + 3x + 2 = 0$ represents

✓
A parabola
B
An ellipse
C
A hyperbola
D
A circle

✓

Answer

Correct option: A.

A parabola

a
(a) $\Delta = (1)\,(1)\,(2) + 2\,\left( {\frac{3}{2}} \right)\,(0)( - 1) - (1)\,{(0)^2} - $$(1)\,{\left( {\frac{3}{2}} \right)^2} - 2{( - 1)^2}$

$ = 2 - \frac{9}{4} - 2 < 0$ and ${h^2} - ab = 1 - 1 = 0$.

i.e., ${h^2} = ab$ ==> a parabola.

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