Question

If $\frac{x^2}{36}-\frac{y^2}{k^2}=1$ is a hyperbola then which of the following statement can be true?

• A. (-3, 1) lies on the hyperbola
• B. (3, 1) lies on the hyperbola
• C. (10, 4) lies on the hyperbola
• D. (5, 2) lies on the hyperbola

Answer 1

The correct option is C

(10, 4) lies on the hyperbola

Given equation of hyperbola is,

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

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

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

We know that,

$k^2>0$

i.e., $\frac{36y^2}{x^2-36}>0$

This condition is satisfied only for (10,4)

Hence (c) is the right answer.