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  • The normal to the hyperbola meets the axes at M and N, and lines MP&

The normal to the hyperbola \mathrm{x^2-2 y^2=2} meets the axes at M and N, and lines MP and NP are drawn at right angles to the axes. The locus of P is \mathrm{2 x^2-y^2=\lambda}, where \mathrm{\lambda} is __________.

Option: 1

8


Option: 2

9


Option: 3

0


Option: 4

5


Answers (1)

best_answer

The normal to

\mathrm{ \frac{x^2}{2}-y^2=1 \text { is } \frac{\sqrt{2} x}{\sec \theta}+\frac{y}{\tan \theta}=2+1=3 }

It meets the axes at \mathrm{M\left(\frac{3 \sec \theta}{\sqrt{2}}, 0\right)}and  \mathrm{N(0,3 \tan \theta)} 

The locus of P is given by

\mathrm{ x=\frac{3 \sec \theta}{\sqrt{2}}, y=3 \tan \theta \quad \therefore 2 x^2-y^2=9 \therefore \lambda=9 }

Posted by

manish

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