Hyperbola · Mathematics · NDA

What is the distance between the foci of the hyperbola $x ^ 2 - 4y ^ 2 = 1$

. What is the distance between the two foci of the hyperbola 25x² - 75y ²= 225 ?

Consider the following in respect of the equation $\frac{x^2}{24-k}+\frac{y^2}{k-16}=2$.

1. The equation represents an ellipse if k = 19.

2. The equation represents a hyperbola if k = 12.

3. The equation represents a circle if k = 20.

How many of the statements given above are correct?

Consider the following statements in respect of hyperbola $\frac{x^2}{\cos ^2 \theta}-\frac{y^2}{\sin ^2 \theta}=1$ :

1. The two foci are independent of θ.

2. The eccentricity is sec θ.

3. The distance between the two foci is 2 units.

How many of the statements given above are correct?

If any point on a hyperbola is (3tan θ, 2sec θ), then what is the eccentricity of the hyperbola?