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  • The locus of the point of intersection of tangents drawn at the extremities of normal chords to hyperbola <span s

The locus of the point of intersection of tangents drawn at the extremities of normal chords to hyperbola \mathrm{xy=c^{2}} 

Option: 1

\mathrm{\left(x^2-y^2\right)^2+4 c^2 x y=0 }


Option: 2

\mathrm{\left(x^2+y^2\right)^2+4 c^{2} x y=0}


Option: 3

\mathrm{\left(x^2-y^2\right)^2+4 c x y=0}


Option: 4

\mathrm{\left(x^2+y^2\right)^2+4 c x y= 0}


Answers (1)

best_answer

Polar is \mathrm{x y_1+x_1 y=2 c^2} ------(1)

Let  normal chord at (h,k) be 

\mathrm{h x-k y=h^2-k^2} -----------(2)

From 1 and 2 \mathrm{\frac{h}{y_1}=\frac{-k}{x_1}=\frac{h^2-k^2}{2 c^2}=\lambda}

And \mathrm{h k=c^2} eliminate \mathrm{h, k} and \mathrm{\lambda}

Posted by

Suraj Bhandari

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