Question

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

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

Answer 1

The Correct Option is D

Given, $\frac{x^{2}}{36} - \frac{y^{2}}{k^{2}} = 1$
$ \Rightarrow \frac{y^{2}}{k^{2}} = \frac{x^{2}}{36} -1 $
$ \Rightarrow k^{2} = \frac{36 y^{2}}{x^{2} -36}$
$ k^{2} >\,0$
If $ x^{2} - 36 > \,0 $
$ \Rightarrow x^{2} >\, 36 $
This is true only for point $(10, 4)$ So, $(10, 4)$ lies on the hyperbola