The eccentricity of a hyperbola passing through the points (3, 0)… - Vidyadip

MCQ

The eccentricity of a hyperbola passing through the points $(3, 0)$, $(3\sqrt 2 ,\;2)$ will be

A
$\sqrt {13} $
✓
$\frac{{\sqrt {13} }}{3}$
C
$\frac{{\sqrt {13} }}{4}$
D
$\frac{{\sqrt {13} }}{2}$

✓

Answer

Correct option: B.

$\frac{{\sqrt {13} }}{3}$

b
(b) $\frac{9}{{{a^2}}} = 1$

==> $a = 3$ and $\frac{{18}}{{{a^2}}} - \frac{4}{{{b^2}}} = 1$

==> ${b^2} = 4$

Therefore, $e = \sqrt {1 + \frac{4}{9}} = \frac{{\sqrt {13} }}{3}$.

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 STD 11 - 10.2 parabola,ellipse,hyperbola→STD 11 - 10.2 parabola,ellipse,hyperbola — all question types→Maths STD 11 Science question papers→CBSE Board STD 11 Science question papers→CBSE Board question paper generator→

Similar questions

Lets $S=\{z \in C:|z-1|=1$ and $(\sqrt{2}-1)(z+\bar{z})-i(z-\bar{z})=2 \sqrt{2}\}$. Let $\mathrm{z}_1, \mathrm{z}_2$ $\in S$ be such that $\left|z_1\right|=\max _{z \in S}|z|$ and $\left|z_2\right|=\min _{z \in S}|z|$. Then $\left|\sqrt{2} z_1-z_2\right|^2$ equals :

Two candidates attempt to solve the equation ${x^2} + px + q = 0$. One starts with a wrong value of p and finds the roots to be $2$ and $6$ and the other starts with a wrong value of $q$ and find the roots to be $2$ and $-9$. The roots of the original equation are

Let $A=\{n \in N: H . C . F .(n, 45)=1\}$ and Let $B=\{2 k: k \in\{1,2, \ldots, 100\}\}$. Then the sum of all the elements of $A \cap B$ is

If $ \text{aN} = \frac{\text{ax}}{\text{x}\in\text{N}}$ and $\text{bN}\cap\text{cN}=\text{d}\text{N}$ Where $ \text{b}, \text{c }\in\text{ N}$

If $\tan\text{x}+\sec\text{x}=\sqrt{3},0<\text{x}<\pi,$ then x is equal to:

Find the sum of series $6^3+ 7^3+…..…..+ 20^3$.

If $z$ is a complex number in the Argand plane, then the equation $|z - 2| + |z + 2| = 8$ represents

If $A = \{ 2,\,4,\,5\} ,\,\,B = \{ 7,\,\,8,\,9\} ,$ then $n(A \times B)$ is equal to

A circle with radius $12$ lies in the first quadrant and touches both the axes, another circle has its centre at $(8,9)$ and radius $7$. Which of the following statements is true

Suppose that all the terms of an arithmetic progression ($A.P.$) are natural numbers. If the ratio of the sum of the first seven terms to the sum of the first eleven terms is $6: 11$ and the seventh term lies in between $130$ and $140$ , then the common difference of this $A.P.$ is