The eccentricity of the conic x^2 - 4 y^2 = 1, is - Vidyadip

MCQ

The eccentricity of the conic ${x^2} - 4{y^2} = 1$, is

A
$\frac{2}{{\sqrt 3 }}$
B
$\frac{{\sqrt 3 }}{2}$
C
$\frac{2}{{\sqrt 5 }}$
✓
$\frac{{\sqrt 5 }}{2}$

✓

Answer

Correct option: D.

$\frac{{\sqrt 5 }}{2}$

d
(d) Given conic is $\frac{{{x^2}}}{{{{(1)}^2}}} - \frac{{{y^2}}}{{{{\left( {\frac{1}{2}} \right)}^2}}} = 1$

$\therefore {b^2} = {a^2}({e^2} - 1)$

$⇒$ $\frac{1}{4} + 1 = {e^2}$

$⇒$ $e = \frac{{\sqrt 5 }}{2}$.

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 "MCQ" from 10.2 parabola,ellipse,hyperbola→10.2 parabola,ellipse,hyperbola — all question types→MATHS STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

Below are four equations in $x$. Assume that $0 < r < 4$. Which of the following equations has the largest solution for $x$ ?

The number of values of $x$ in the interval $\left(\frac{\pi}{4}, \frac{7 \pi}{4}\right)$ for which $14 \operatorname{cosec}^{2} x-2 \sin ^{2} x=21$ $-4 \cos ^{2} x$ holds, is

Two dice are thrown:
P is the event that the sum of the scores on the uppermost faces is a multiple of 6.
Q is the event that the sum of the scores on the uppermost faces is at least 10.
R is the event that same scores on both dice. Which of the following pairs is mutually exclusive?

What is the standard deviation of the following series

class	$0-10$	$10-20$	$20-30$	$30-40$
Freq	$1$	$3$	$4$	$2$

The general solution of the equation $7\cos^2\text{x}+3\sin^2\text{x}=4$ is:

The equation of the lines which passes through the point $(3, -2)$ and are inclined at ${60^o}$ to the line $\sqrt 3 x + y = 1$

Let $a \ne b,\,c \ne 0$ and $x^2 + ax + bc = 0$ and $x^2 + bx + ac = 0$ have a common root then

Statement $-1$ : Equation of other roots is $x^2 + cx + ab = 0$

Statement $-2$ : $a + b + c = 0$

The ends of the base of an isosceles triangle are at $(2a,\;0)$ and $(0,\;a).$ The equation of one side is $x=2a$ The equation of the other side is

The following data has been arranged in ascending order. If their median is 63, find the value of x.34, 37, 53, 55, x, x + 2, 77, 83, 89 and 100.

Two fixed points are $A(a,0)$ and $B( - a,0)$. If $\angle A - \angle B = \theta $, then the locus of point $C$ of triangle $ABC$ will be