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  • Normal to a rectangular hyperbola at P meets the transverse axis at N. If foci of hyperbola are S and S, then if the value of <img alt="\mathrm{\frac{S N}{S P}}" src="https://entrancecorner.oncodec

Normal to a rectangular hyperbola at P meets the transverse axis at N. If foci of hyperbola are S and S, then if the value of \mathrm{\frac{S N}{S P}} is \mathrm{\sqrt{k}} , then k is

Option: 1

\sqrt{2}


Option: 2

\sqrt{3}


Option: 3

\sqrt{-2}


Option: 4

-\sqrt{4}


Answers (1)

best_answer

We know that P N is angle bisector of focal radii S P and S P.

\begin{aligned} &\mathrm{ \therefore \frac{S P}{S^{\prime} P}=\frac{S N}{S^{\prime} N} }\\ &\mathrm{ \therefore \frac{S N}{S P}=\frac{S^{\prime} N}{S^{\prime} P}=\left|\frac{S N-S^{\prime} N}{S P-S^{\prime} P}\right|=\frac{S S^{\prime}}{\left|S P-S^{\prime} P\right|}=e=\sqrt{2}}\\ \end{aligned}

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shivangi.bhatnagar

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