If the vertices of a hyperbola be at $\left ( -2,0 \right )$ and $\left ( 2,0 \right )$ and one of its foci be at $\left ( -3,0 \right )$, then which one of the following points does not lie on this hyperbola ? Option 1)$\left ( 4,\sqrt{15} \right )$      Option 2)$\left ( 2\sqrt{6},5 \right )$Option 3)$\left ( 6,5\sqrt{2} \right )$Option 4)$\left ( -6,2\sqrt{10} \right )$

Standard equation of parabola -

$y^{2}=4ax$

- wherein

Given, equation of hyperbola  $\frac{x^{2}}{4}-\frac{y^{2}}{b^{2}}=1$

Given

$ae=-3$

$=>b^{2}=a^{2}e^{2}-a^{2}$

put a = 2

$=>b^{2}=5$

Hence , equation of hyperbola is

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

Hence $(6,5\sqrt2)$ does not lie on hyperbola.

Option 1)

$\left ( 4,\sqrt{15} \right )$

Option 2)

$\left ( 2\sqrt{6},5 \right )$

Option 3)

$\left ( 6,5\sqrt{2} \right )$

Option 4)

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

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