Locus of the $$mid-point$$ of the chord of the hyperbola $$x2a2-y2b2=1$$ which is a tangent to the circle $$x2+y2=c2$$ is

Correct option is 1x2a2-y2b22=c2x2a4+y2b4

Questions

Locus of the mid-point of the chord of the hyperbola $\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1$ which is a tangent to the circle $x^{2} + y^{2} = c^{2}$ is

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x2a2-y2b22=c2x2a4+y2b4

x2a2+y2b22=c2x2a4-y2b4

x2a2-y2b2=c2x2a2+y2b22

x2a4-y2b4=c2x2a2+y2b22

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detailed solution

Correct option is A

Let (h, k) be the mid-point of the chord, then its equation ishxa2-kyb2=h2a2-k2b2Since it touches the circle x2+y2=c2h2a2-k2b2ha22+kb22=±c⇒h2a2-k2b22=c2h2a4+k2b4Required locus is x2a2-y2b22=c2x2a4+y2b4

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Locus of the mid-point of the chord of the hyperbola x2a2-y2b2=1 which is a tangent to the circle x2+y2=c2 is

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Locus of the mid-point of the chord of the hyperbola $\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1$ which is a tangent to the circle $x^{2} + y^{2} = c^{2}$ is