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

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Question

equation of hyperbola is $\frac{{{x^2}}}{4} - \frac{{{y^2}}}{{{b^2}}} = 1$ and $ae = 3$

We know that ${a^2}{e^2} = {a^2} + {b^2}$

Vedclass · Accepted Answer

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

Vedclass · Answer

equation of hyperbola is $\frac{{{x^2}}}{4} - \frac{{{y^2}}}{{{b^2}}} = 1$ and $ae = 3$

We know that ${a^2}{e^2} = {a^2} + {b^2}$

$9 = 4 + {b^2} \Rightarrow {b^2} = 5$ Hence equation of hyperbola is $\frac{{{x^2}}}{4} - \frac{{{y^2}}}{5} = 1\,$

Hence $\left( {6,5\sqrt 2 } \right)$ does not lie on $\frac{{{x^2}}}{4} - \frac{{{y^2}}}{5} = 1\,$

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?

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