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A tangent to the hyperbola (x^2)/(a^2)-(...

A tangent to the hyperbola `(x^2)/(a^2)-(y^2)/(b^2)=1` cuts the ellipse `(x^2)/(a^2)+(y^2)/(b^2)=1` at `Pa n dQ` . Show that the locus of the midpoint of `P Q` is `((x^2)/(a^2)+(y^2)/(b^2))^2=(x^2)/(a^2)-(y^2)/(b^2)dot`

A

`((x^(2))/(a^(2))+(y^(2))/(b^(2)))^(2)=(x^(2))/(a^(2))-(y^(2))/(b^(2))`

B

`((x^(2))/(a^(2))-(y^(2))/(b^(2)))^(2)=(x^(2))/(a^(2))+(y^(2))/(b^(2))`

C

`((x^(2))/(a^(2))-(y^(2))/(b^(2)))^(2)=(2x^(2)y^(2))/(a^(2)b^(2))`

D

none of these

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OBJECTIVE RD SHARMA ENGLISH-HYPERBOLA-Chapter Test
  1. If the tangent at (h, k) on b^2x^2-a^2y^2=a^2b^2 cuts the auxiliary ci...

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  2. If the chords of contact of tangents drawn from P to the hyperbola x^(...

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  3. The tangent at a point P on the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(...

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  4. The mid-point of the chord intercepted by the hyperbola 9x^(2)-16y^(2)...

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  5. Locus of P such that the chord of contact of P with respect to y^2=4ax...

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  6. C is the center of the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 The tangen...

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  7. If lx+my+n=0 is a tangent to the rectangular hyperbola xy=c^(2), then

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  8. A tangent to the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 cuts the ellipse ...

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  9. The product of lengths of perpendicular from any point on the hyperbol...

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  10. The angle between the asymptotes of the hyperbola 3x^(2)-y^(2)=3, is

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  11. Find the area of the triangle formed by any tangent to the hyperbola (...

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  12. If e1a n d\ e2 are respectively the eccentricities of the ellipse (x^2...

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  13. The distance between the directrices of the hyperbola x=8s e ctheta,\ ...

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  14. The straight line x+y=sqrt(2)p will touch the hyperbola 4x^(2)-9y^(2)=...

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  15. The locus of the point of intersection of perpendicular tangents to th...

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  16. .Find the product of lengths of the perpendiculars from any point on t...

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  17. The angle between the asymptotes of the hyperbola 27x^(2)-9y^(2)=24, i...

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  18. The equation of the chord of contact of tangents from (1,2) to the hyp...

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  19. Equation of the hyperbola whose vertices are (+-3,0) and foci at (+-5,...

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  20. The length of the semi-transverse axis of the rectangular hyperbola xy...

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