MCQ
The equation $14{x^2} - 4xy + 11{y^2} - 44x - 58y + 71 = 0$ represents
  • A
    A circle
  • An ellipse
  • C
    A hyperbola
  • D
    A rectangular hyperbola

Answer

Correct option: B.
An ellipse
b
(b) Check $\Delta \ne 0$ and ${h^2} < ab$.

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

Similar questions

If $\sin 5x + \sin 3x + \sin x = 0$, then the value of $x$ other than $0$ lying between $0 \le x \le \frac{\pi }{2}$ is
The maximum value of $z$ in the following equation $z=6 x y+y^{2},$ where $3 x+4 y \leq 100$ and $4 x+3 y \leq 75$ for $x \geq 0$ and $y \geq 0$ is $......$
An equilateral triangle is inscribed in the parabola ${y^2} = 4ax$ whose vertices are at the parabola, then the length of its side is equal to
If $L=\sin ^{2}\left(\frac{\pi}{16}\right)-\sin ^{2}\left(\frac{\pi}{8}\right)$ and $M=\cos ^{2}\left(\frac{\pi}{16}\right)-\sin ^{2}\left(\frac{\pi}{8}\right),$ then 
A line passes through the origin and makes equal angles with the positive coordinate axes. It intersects the lines
$
L_1: 2 x+y+6=0 \text { and } L_2: 4 x+2 y-p=0, p>0
$
at the points $A$ and $B$, respectively. If $A B=\frac{9}{\sqrt{2}}$ and the foot of the perpendicular from the point A on the line $L_2$ is $M$, then $\frac{A M}{B M}$ is equal to
Let $a,b,c$ be positive real numbers. The following system of equations in $x, y$  and $ z $ $\frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}} - \frac{{{z^2}}}{{{c^2}}} = 1$, $\frac{{{x^2}}}{{{a^2}}} - \frac{{{y^2}}}{{{b^2}}} + \frac{{{z^2}}}{{{c^2}}} = 1, - \frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}} + \frac{{{z^2}}}{{{c^2}}} = 1$ has
Let $f : X \rightarrow Y$ be a function such that $f(x) = \sqrt{x - 2} + \sqrt{4 - x} ,$ then the set of $X$ and $Y$ for which $f(x)$ is both injective as well as surjective, is-
The values of $x$ and $y$ satisfying the equation $\frac{{(1 + i)x - 2i}}{{3 + i}}$ $ + \frac{{(2 - 3i)\,y + i}}{{3 - i}} = i$ are
Let $\bar{a}=\hat{i}+\hat{j}+\hat{k}, \vec{b}$ and $\vec{c}=\hat{j}-\hat{k}$ be three vectors such that $\vec{a} \times \vec{b}=\vec{c}$ and $\vec{a} \cdot \vec{b}=1$. If the length of projection vector of the vector $\vec{b}$ on the vector $\vec{a} \times \vec{c}$ is $l$, then the value of $3l^{2}$ is equal to $.....$
A circle touches the $x$ - axis and also touches the circle with centre at $(0, 3)$ and radius $2$. The locus of the centre of the circle is