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

Question

Dr. Abubacker · Accepted Answer

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

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

Explanation

Reviewed by Dr. Abubacker

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