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

Question

Find the equation of the hyperbola with:
$\text{Vertices }(0,\pm7),\text{ e}=\frac{4}{3}$

✓

Answer

$\text{Vertices }(0,\pm7),\text{ e}=\frac{4}{3}$
$\therefore\ \text{b}=7,\text{ e}=\frac{4}{3}$
Now, $\text{a}^2=\text{b}^2(\text{e}^2-1)$
$=49\Big(\frac{16}{9}-1\Big)=\frac{343}{9}$
So, the equation of hyperbola is,
$\frac{\text{x}^2}{\text{a}^2}-\frac{\text{y}^2}{\text{b}^2}=-1$
$\Rightarrow\frac{\text{x}^2}{\frac{343}{9}}-\frac{\text{y}^2}{49}=-1$
$\Rightarrow9\text{x}^2-7\text{y}^2+343=0$

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→Rajasthan Board STD 11 Science question papers→Rajasthan Board question paper generator→

Similar questions

Find the sum of all integers between 84 and 719, which are multiples of 5.

If $C_0, C_1, C_2, \ldots \ldots \ldots . C_n$ are the binomial coefficients in the expansion of $(1+x)^n$, then prove that :
$2 C_0+\frac{2^2 C_1}{2}+\frac{2^3 C_2}{3}+\ldots \ldots +\frac{2^{n+1} \cdot C_n}{n+1}=\frac{3^{n+1}-1}{n+1}$

Calculate the value of $\lim _{x \rightarrow a} \frac{a \sin x-x \sin a}{a x^2-a^2 x}.$

Evaluate the following limit:
$\lim\limits_{\text{x}\rightarrow0}\frac{\text{e}^\text{x}-\text{x}-1}{2}$

Find the point on $Z-axis$ which is equidistant from points $A(1,5,7)$ and $B(5,1,-4)$.

Reduce the equation $\sqrt{3}\text{x}+\text{y}+2=0$ to:
The normal form and find p and $\alpha.$

A die is thrown twice Each time the number appearing on it is recorded Describe the following events:
C = sum of the numbers is less than
Also, find A ∪ B, A ∩ B, A ∪ C, A ∩ C Which pairs of events are mutually exclusive?

Solve the inequality $\frac{1}{2}\left(\frac{3 x}{5}+4\right) \geq \frac{1}{3}(x-6)$ for real x.

Two dice are thrown. find the odds in favour of getting the sum:

5.

Evaluate $\mathop {\lim }\limits_{x \to 0} ({\text{cosec }}x - \cot x)$