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Prove that the locus of the mid -points ...

Prove that the locus of the mid -points of the chords of the circle `x^(2)+y^(2)=16` which are tangents to the hyperbola `9x^(2)-16y^(2)=144` is `(x^(2)+y^(2))^(2)=16x^(2)-9y^(2)`.

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AAKASH SERIES-HYPERBOLA-Additional Exercise
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  2. Find the locus of the point of intersection of two tangents to the hyp...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  18. A hyperbola having the transverse axis of length 2 sin theta, is confo...

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  19. An ellipse has eccentricity 1/2 and the focus at the point P(1/2,1). I...

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  20. The locus represented by x=(a)/(2)(t+(1)/(t)),y=(a)/(2)(t-(1)/(t)) i...

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