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Chords of the hyperbola x^(2)-y^(2)=a^(2...

Chords of the hyperbola `x^(2)-y^(2)=a^(2)` touch the parabola `y^(2)=4ax`. Prove that the locus of their middle-points is the curve `y^(2)(x-a)=x^(3)`.

A

`x^(2)(y-a)=y^(3)`

B

`y^(2)(x-a)=x^(3)`

C

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

D

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

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OBJECTIVE RD SHARMA ENGLISH-HYPERBOLA-Chapter Test
  1. The equation of the pair of asymptotes of the hyperbola xy-4x+3y=0, is

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  2. If the latus rectum of the hyperbola (x^(2))/(16)-(y^(2))/(b^(2))=1 is...

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  3. Chords of the hyperbola x^(2)-y^(2)=a^(2) touch the parabola y^(2)=4ax...

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  4. Tangents drawn from the point (c, d) to the hyperbola (x^(2))/(a^(2))-...

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  5. If the tangent at (h, k) on b^2x^2-a^2y^2=a^2b^2 cuts the auxiliary ci...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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