Find the equation of hyperbola which has Vertices ( 7,0),e = 4 3 - Vidyadip

Question

Find the equation of hyperbola which has Vertices $( \pm 7,0),e = \frac{4}{3}$

✓

Answer

Here vertices are $(± 7, 0)$ which lie on x-axis.
So the equation of hyperbola in standard form is $\frac{{{x^2}}}{{{a^2}}} - \frac{{{y^2}}}{{{b^2}}} = 1$
$\therefore$ Vertices $(± a, 0)$ is $(± 7, 0) ⇒ a = 7$
Now $e = \frac{4}{3} \Rightarrow \frac{c}{a} = \frac{4}{3} \Rightarrow \frac{c}{7} = \frac{4}{3} \Rightarrow c = \frac{{28}}{3}$
We know that $c^2 = a^2 + b^2$
$\therefore {\left( {\frac{{28}}{3}} \right)^2} = {(7)^2} + {b^2} \Rightarrow {b^2} = \frac{{784}}{9} - 49 = \frac{{343}}{9}$
Thus required equation of hyperbola is
$\frac{{{x^2}}}{{{{(7)}^2}}} - \frac{{{y^2}}}{{\frac{{343}}{9}}} = 1 \Rightarrow \frac{{{x^2}}}{{49}} - \frac{{{9y^2}}}{{343}} = 1$

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 "2 Marks Questions" 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

There are four men and, six women on the city council. If one council member is selected for a committee at random, how likely is it that it is a woman?

Two dice are thrown. The events $A, B, C, D, E$ and $F$ are described as follows:
A = Getting an even number on the first die.
B = Getting an odd number on the first die.
C = Getting at most $5$ as sum of the numbers on the two dice.
D = Getting the sum of the numbers on the dice greater than 5 but less than 10.
E = Getting at least $10$ as the sum of the numbers on the dice.
F = Getting an odd number on one of the dice.
Describe the following events:
$A$ and $B, B$ or $C, B$ and $C, A$ and $E, A$ or $F, A$ and $F$.

Find the value of $n$ such that :
(i) ${ }^n P _5=42{ }^n P _3, n>4$
(ii) $\frac{{ }^n P _4}{{ }^{n-1} P _4}=\frac{5}{3}, n>4$

Solve the following system of equations in R.
$\frac{2\text{x}+1}{7\text{x}-1}>5,\frac{\text{x}+7}{\text{x}-8}>2$

Find the coordinates of the foci, and the vertices, the eccentricity and the length of the latus rectum of the hyperbolas.
$\frac{{{x^2}}}{{16}} - \frac{{{y^2}}}{9} = 1$

Differentiate the following function with respect to $(\text{x})$:$2\sec\text{x}+3\cot\text{x}-4\tan\text{x}$

If U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {2, 4, 6, 8} and B= {2, 3, 5, 7}, verify that: (A $\cup$ B)' = A' $\cap$ B'

A card is drawn at random from a pack of 52 cards, find the probability that the card drawn is:Neither an ace nor a king

For the relation $R_1$ defined on $R$ by the rule $(\text{a, b})\in\text{R}_1\Leftrightarrow1+\text{ab}>0$
Prove that, $(\text{a, b})\in\text{R}_1$ and $(\text{a},\text{b})\in\text{R}_1$ and $(\text{b},\text{c})\in\text{R}_1\Rightarrow(\text{a, c})\in\text{R}_1$ is not true for all $\text{a, b, c}\in\text{R}$

Find the derivative of $1/x^2$ from the first principle.