Question

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

• A. A parabola
• B. An ellipse
• C. A hyperbola
• D. A circle

Answer 1

Answer: (A)

A parabola

Answer 2

Comparing the given equation with

$a x ^ { 2 } + 2 h x y + b y ^ { 2 } + 2 g x + 2 f y + c = 0$

Here, a = 1, b = 1, h = – 1, $g = \frac { 3 } { 2 }$, f = 0, c = 2

Now $\Delta = a b c + 2 f g h - a f ^ { 2 } - b g ^ { 2 } - c h ^ { 2 }$

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

$h ^ { 2 } - a b = 1 - 1 = 0$ i.e., $h ^ { 2 } = a b$

So given equation represents a parabola