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If the vertices of a hyperbola be at (-2,0)

Question:

If the vertices of a hyperbola be at $(-2,0)$ and $(2,0)$ and one of its foci be at $(-3,0)$, then which one of the following points does not lie on this hyperbola?

  1. $(4, \sqrt{15})$

  2. $(-6,2 \sqrt{10})$

  3. $(6,5 \sqrt{2})$

  4. $(2 \sqrt{6}, 5)$


Correct Option: , 3

Solution:

$\mathrm{ae}=3, \mathrm{e}=\frac{3}{2}, \mathrm{~b}^{2}=4\left(\frac{9}{4}-1\right), \mathrm{b}^{2}=5$

$\frac{x^{2}}{4}-\frac{y^{2}}{5}=1$

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