Transverse Axis of Hyperbola

Q. Which of the following is true regarding hyperbola $\frac{y^2}{b^2}-\frac{x^2}{a^2}=1?$

1. $y$-axis is transverse axis.
2. The given hyperbola do not intersect the x-axis
3. All of the above
4. Vertices are $(0,b)\text{and}(0,-b)$

Q.

In a given standrard hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$.What is the length of transverse axis?

1. 2a

2. 2b

3. a

4. b

Q.

The transverse axis of a hyperbola is double the conjugate axes. Whats the eccentricity of the hyperbola

1. $\frac{\sqrt{5}}{4}$

2. $\frac{\sqrt{7}}{4}$

3. $\frac{7}{4}$

4. $\frac{5}{3}$

Q.

The transverse axis of a hyperbola is double the conjugate axes. Whats the eccentricity of the hyperbola

1. $\frac{\sqrt{5}}{4}$

2. $\frac{\sqrt{7}}{4}$

3. $\frac{7}{4}$

4. $\frac{5}{3}$

Q. A hyperbola has its centre at the origin, passes through the point $(4,2)$ and has transverse axis of length $4$ along the $x$-axis. Then the eccentricity of the hyperbola is :

1. $\sqrt{3}$
2. $\frac{2}{\sqrt{3}}$
3. $2$
4. $\frac{3}{2}$

Q. The equation of hyperbola with vertices at $(0,\pm 6)$ and $e=\frac{5}{3}$
(where $e$ is eccentricity)

1. $\frac{y^2}{36}-\frac{x^2}{64}=1$

2. $\frac{x^2}{64}-\frac{y^2}{36}=1$
3. $\frac{x^2}{36}-\frac{y^2}{64}=1$
4. $\frac{y^2}{35}-\frac{x^2}{25}=1$

Q. The eccentricity of the hyperbola whose length of conjugate axis is equal to half of the distance between its foci is $e$, then $3e^2=$