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  • A hyperbola whose transverse axis is along the major axis of the conic <img alt="\frac{x^{2}}{3}+\frac{y^{2}}{4}=4" src="http://entrancecorner.oncodecogs.com/gif.latex?%5Cdpi%7B100%7D%20%

A hyperbola whose transverse axis is along the major axis of the conic

\frac{x^{2}}{3}+\frac{y^{2}}{4}=4and has vertices at the foci of this conic.  If the eccentricity of the

hyperbola is \frac{3}{2} then which of the following points does NOT lie on it ?

Option: 1

(0,2)


Option: 2

(\sqrt{5},2\sqrt{2})


Option: 3

(\sqrt{10},2\sqrt{3})


Option: 4

(5,2\sqrt{3})


Answers (1)

best_answer

\\\text { ellipse } \frac{x^{2}}{12}+\frac{y^{2}}{16}=1 \\ \text { foci }(0, \pm \text { be }) \\ e_{1}=\sqrt{1-\frac{12}{16}}=\frac{1}{2}

the eccentricity of the hyperbola

\\e_2=\frac{3}{2}\\

\\\text { equation } \Rightarrow \frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=-1 \\ e_{2}=\frac{3}{2}=\sqrt{1+\frac{a^{2}}{b^{2}}} \quad\\ \Rightarrow \quad \frac{9}{4}-1=\frac{a^{2}}{b^{2}} \\\Rightarrow \frac{a^{2}}{b^{2}}=\frac{5}{4} \quad\\ \Rightarrow \quad a^{2}=5 \\\Rightarrow \frac{x^{2}}{5}-\frac{y^{2}}{4}=-1

Clearly point (5,2\sqrt3) does not lies on it.

Posted by

Ajit Kumar Dubey

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