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.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

JEE STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

The equation of the circle having the lines ${x^2} + 2xy + 3x + 6y = 0$ as its normals and having size just sufficient to contain the circle $x(x - 4) + y(y - 3) = 0$is

If $\omega $ is a complex cube root of unity, then the determinant $\left| {\,\begin{array}{*{20}{c}}2&{2\omega }&{ - {\omega ^2}}\\1&1&1\\1&{ - 1}&0\end{array}\,} \right| = $

$\mathop {\lim }\limits_{x \to {1^ - }} \frac{{\sqrt \pi - \sqrt {2\,{{\sin }^{ - 1}}x} }}{{\sqrt {1 - x} }}$ is equal to

The probabilities of winning the race by two athletes $A$ and $B$ are $\frac{1}{5}$ and $\frac{1}{4}.$ The probability of winning by neither of them, is

Let $a $ and $ b$ be two unit vectors inclined at an angle $\theta $, then $\sin \,(\theta /2)$ is equal to

The area enclosed by the curves $y^2+4 x=4$ and $y-2 x=2$ is :

Let $\vec{a}$ and $\vec{b}$ be two vectors such that $|\vec{a}|=1,|\vec{b}|=4$ and $\vec{a} \cdot \vec{b}=2$. If $\vec{c}=(2 \vec{a} \times \vec{b})-3 \vec{b}$ and the angle between $\vec{b}$ and $\vec{c}$ is $\alpha$, then $192 \sin ^2 \alpha$ is equal to

Consider the quadratic equation $\left( {c - 5} \right)\,{x^2} - 2cs + \left( {c - 4} \right) = 0$, $c \ne 5$. Let $S$ be the set of all integral values of $c$ for which one root of the equation lies in the interval $(0, 2)$ and its other root lies in the interval $(2, 3)$. Then the number of elements in $S$ is

${d \over {dx}}\{ {(\sin x)^{\log x}}\} = $

The conjugate of $\frac{{{{(2 + i)}^2}}}{{3 + i}},$ in the form of $a + ib$, is