R D Sharma Solutions for Chapter: Hyperbola, Exercise 2: VERY SHORT ANSWER QUESTIONS (VSAQs)

The eccentricity of the hyperbola whose latus-rectum is half of its transverse axis is $\sqrt{\frac{k}{2}}$

Find the value of $k$

Write the equation of the hyperbola of eccentricity $\sqrt{2},$ if it is known that the distance between its foci is $16.$

If the foci of the ellipse $\frac{x^2}{16}+\frac{y^2}{b^2}=1$ and the hyperbola $\frac{x^2}{144}-\frac{y^2}{81}=\frac{1}{25}$ coincide, write the value of $b^2.$

Write the length of the latus-rectum of the hyperbola $16x^2-9y^2=144.$

If the latus-rectum through one focus of a hyperbola subtends a right angle at the farther vertex, then write the eccentricity of the hyperbola.

Distance between the directrices of the hyperbola is $k\sqrt{2}$ where  $x = 8 \sec \theta$, $y = 8$ $\tan$ $\theta .$

Then find the value of $k$.

Write the equation of the hyperbola whose vertices are $(\pm 3, 0)$ and foci at $(\pm 5, 0).$

If $e_1$ and $e_2$ are respectively the eccentricities of the ellipse $\frac{x^2}{18}+\frac{y^2}{4}=1$ and the hyperbola $\frac{x^2}{9}-\frac{y^2}{4}=1$, then write the value of $2e_1^2+e_2^2$.