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  • The locus of the point the chord of contact of tangents from which to the hyperbola touches the circle on the line joining the foci as diameter isOption: 1</stro

The locus of the point the chord of contact of tangents from which to the hyperbola touches the circle on the line joining the foci as diameter is

Option: 1

\mathrm{\frac{x^2}{a^4}+\frac{y^2}{b^4}=\frac{1}{a^2+b^2}}


Option: 2

\mathrm{\frac{x^2}{a^4}-\frac{y^2}{b^4}=\frac{1}{a^2+b^2}}


Option: 3

\mathrm{\frac{x^2}{a^4}+\frac{y^2}{b^4}=\frac{1}{a^2-b^2}}


Option: 4

\text { None of these }


Answers (1)

If (h, k) be the point, then chord of contact is

\mathrm{\frac{h x}{a^2}-\frac{k y}{b^2}=1}. It touches the circle on the join of (a e, 0)

and (-a e, 0) as diameter

or \mathrm{x^2+y^2=a^2 e^2=a^2+b^2\, \, Apply \, \, p=r}

\mathrm{ \begin{aligned} & \therefore \frac{1}{\sqrt{\left(\frac{h^2}{a^4}+\frac{k^2}{b^4}\right)}}=\sqrt{a^2+b^2} \\ & \therefore \text { Locus is } \frac{x^2}{a^4}+\frac{y^2}{b^4}=\frac{1}{a^2+b^2} \end{aligned} }

Posted by

Kshitij

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