Conjugate Axis of Hyperbola

Q.

Find the equation of the hyperbola satisfying the given conditions.
Foci (4, 0), the latus rectum is of length 12.

Q.

Equation of the conjugate axis of the hyperbola $5x^2-4y^2-30x-8y-39$ = 0

1. y+1 = 0

2. x-3 = 0

3. x+3 = 0

4. y-1 = 0

Q.

What the eccentricity of the hyperbola with its principal axes along the

coordinate axes and which passes through (3, 0) and $(3\sqrt{2},2)$

1. $\frac{1}{3}$

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

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

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

Q.

In a hyperbola e=2 and the length of semitransverse axis is 3 and the length of conjugate axis is

1. $3\sqrt{3}$

2. $6\sqrt{3}$

3. $6\sqrt{2}$

4. $3\sqrt{2}$

Q.

Select the right options about a hyperbola.

1. Conjugate axis is the axis of the hyperbola that passes through the foci

2. A transverse axis always pass through the origin

3. The straight line through the centre which is perpendicular to the transverse axis doesn't meet hyperbola in real point.

4. Eccentricity is the ratio of 2 distances

Q. The length of the conjugate axis of the hyperbola $9x^2-90x-25y^2+150y-225=0$ is units