Which of the following equations represents a parabola: - Vidyadip

MCQ

Which of the following equations represents a parabola:

A
$(x - y)^3= 3$
B
$\frac{\text{x}}{\text{y}}-\frac{\text{y}}{\text{x}}=0$
✓
$\frac{\text{x}}{\text{y}}+\frac{\text{4}}{\text{x}}=0$
D
$(x + y)^2+ 3 = 0$

✓

Answer

Correct option: C.

$\frac{\text{x}}{\text{y}}+\frac{\text{4}}{\text{x}}=0$

We know that the general equation of parabola is
$y^2= 4ax$
$y^2= -4ax$
$x^2= 4ax$
$x^2= -4ax$
From option $(a),$
$(x - y)^3= 3$
It is not represent the parabola.
From option $(b),$
$\frac{\text{x}}{\text{y}}-\frac{\text{y}}{\text{x}}=0$
$x^2= y^2$
It is not represent the parabola.
From option $(c),$
$\frac{\text{x}}{\text{y}}+\frac{\text{4}}{\text{x}}=0$
$x^2+ 4y = 0$
$x^2= -4y$
So, this is represented the parabola.
From option $(d),$
$(x + y)^3+ 3 = 0$
It is not represent the 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

More "M.C.Q (1 Marks)" from Conic Sections→Conic Sections — all question types→Maths STD 11 Science question papers→CBSE Board STD 11 Science question papers→CBSE Board question paper generator→

Similar questions

Three points $\mathrm{O}(0,0), \mathrm{P}\left(\mathrm{a}, \mathrm{a}^2\right), \mathrm{Q}\left(-\mathrm{b}, \mathrm{b}^2\right), \mathrm{a}>0, \mathrm{~b}>0$, are on the parabola $y=x^2$. Let $S_1$ be the area of the region bounded by the line $P Q$ and the parabola, and $S_2$ be the area of the triangle $O P Q$. If the minimum value of $\frac{\mathrm{S}_1}{\mathrm{~S}_2}$ is $\frac{\mathrm{m}}{\mathrm{n}}, \operatorname{gcd}(\mathrm{m}, \mathrm{n})=1$, then $\mathrm{m}+\mathrm{n}$ is equal to :

The connective in the statement “Earth revolves around the Sun and Moon is a satellite of earth" is:

If $72^x \cdot 48^y=6^{x y}$, where $x$ and $y$ are non-zero rational numbers, then $x+y$ equals

If $z$ is a complex number such that $| z | = 4$ and $arg \,(z) = \frac {5\pi }{6}$ , then $z$ is equal to

Given that x, y and b are real numbers and x < y, b > 0, then:

$\tan \frac{A}{2}$ is equal to

If $y = 3\,sin\,x + 4\,cos\,x$ then find the maximum value of $y$

The three lines $lx + my + n = 0$, $mx + ny + l = 0$, $nx + ly + m = 0$ are concurrent if

Suppose $A B C D(A B \| C D)$ is a trapezium such that the diagonals $AC , BD$ bisect the angles $\angle DAB , \angle CBA$, respectively. Then

The region represented by $\{z=x+i y \in C:|z|-\operatorname{Re}(z) \leq 1\}$ is also given by the inequality