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Let any double ordinate \mathrm{\text { PNP' }} of the hyperbola   \mathrm{\frac{x^2}{25}-\frac{y^2}{16}=1}  be

produced on both sides to meet the asymptotes in \mathrm{Q}  and \mathrm{Q^{\prime} .}

then  \mathrm{P Q \cdot P^{\prime} Q}  is to

Option: 1

25


Option: 2

16


Option: 3

41


Option: 4

none of these


Answers (1)

best_answer

\mathrm{N P=\frac{4}{5} \sqrt{x_1^2-25}}

Point Q is on  

\mathrm{\begin{aligned} & y=\frac{4}{5} x \\ & N Q=\frac{4}{5} x_1 \\ & P Q=N Q-N P \\ & =\frac{4}{5}\left(x_1-\sqrt{x_1^2-25}\right) \\ & P^{\prime} Q=\frac{4}{5}\left(x_1+\sqrt{x_1^2-25}\right) \\ & P Q \cdot P^{\prime} Q=16 \end{aligned}}

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Pankaj

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