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Find the locus of the mid-point of the chord of the hyperbola `x^(2)/a^(2)-y^(2)/b^(2)=1` which subtends a right angle at the origin.

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The correct Answer is:
`(x^2/a^(2)-y^(2)/b^(2)) (1/a^(2)-1/b^(2)) =x^(2)/a^(4)+y^(2)/b^(4)`
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AAKASH SERIES-HYPERBOLA-Additional Exercise
  1. PQ is a double ordinate of the hyperbola x^(2)/a^(2)-y^(2)/b^(2)=1 suc...

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  2. If x= 9 is a chord of contact of the hyperbola x^(2) -y^(2) =9, then ...

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  3. Find the locus of the mid-point of the chord of the hyperbola x^(2)/a^...

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  4. A hyperbola has axes along the coordinate axes. Its trasverse axis is ...

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  5. Find the locus of the point of intersection of two tangents to the hyp...

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  6. Prove that the locus of the mid -points of the chords of the circle x^...

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  7. Find the asymptodes of the hyperbola 2x^(2)+5xy+2y^(2)-11x-7y-4=0

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  8. Find the equation of the hyperbola whose asymptotes are the straight l...

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  9. The equation of the line passing throught the centre of a rectangular ...

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  10. A normal to the hyperbola x^(2)//a^(2) -y^(2)//b^(2) =1 cuts the axes...

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  11. Let P (a sec theta, b tan theta) and Q (a sec phi, b tan theta) where ...

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  12. Prove that the locus of the point of intersection of tangents at the e...

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  13. Prove that the portion of the tangent of the rectangular hyperbola int...

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  14. If the hyperbola xy=c^(2) intersects the circle x^(2)+y^(2)=a^(2)" is ...

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  15. Let P (a sec theta, b tan theta) and Q (a sec phi, b tan theta) where ...

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  16. If x=9 is the chord of contact of tangents of x^(2)-y^(2)=9, then show...

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  17. Show that the equationi of the rectanglar hyperbola whose focus is (1,...

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  18. The hyperbola x^(2)/a^(2)-y^(2)/b^(2)=1 has its conjugate axis 5 and p...

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  19. Tangents are drawn from points on the hyperbola x^(2)/9-y^(2)/4=1 to t...

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  20. If a hyperbola passes through a focus of the ellipse and it transverse...

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