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Prove that the part of the tangent at an...

Prove that the part of the tangent at any point of the hyperbola `(x^2)/(a^2)-(y^2)/(b^2)=1` intercepted between the point of contact and the transvers axis is a harmonic mean between the lengths of the perpendiculars drawn from the foci on the normal at the same point.

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MOTION-HYPERBOLA-EXERCISE-3
  1. Find the equation of the tagent to the hyperbola x^(2)-4y^(2)=36 which...

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  2. Tangents are drawn to the hyperbola 3x^2-2y^2=25 from the point (0,5/2...

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  3. nd are inclined at avgicsTangents are drawn from the point (alpha, bet...

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  4. Let 'p' be the perpendicular distance from the centre C of the hyperbo...

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  5. The tangent & normal at a point on x^2/a^2-y^2/b^2=1 cut the y-axis re...

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  6. Find the locus of the foot of perpendicular from the centre upon any ...

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  7. If the normal at a pont P to the hyperbola x^2/a^2 - y^2/b^2 =1 meets ...

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  8. The normla to the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 drawn at an extr...

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  9. Find the equations of the tangents to the hyperbola x^2=9y^2=9 that ar...

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  10. An ellipse and a hyperbola have their principal axes along the coor...

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

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  12. Prove that the part of the tangent at any point of the hyperbola (x^2)...

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  13. Find the length of the diameter of the ellipse x^(2)/(25)+y^(2)/(9)=1 ...

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  14. The tangent at P on the hyperbola x^(2)/a^(2)-y^(2)/b^(2)=1 meets one ...

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  15. From any point of the hyperbola x^(2)/a^(2)-y^(2)/b^(2)=1, tangents a...

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  16. If two points P & Q on the hyperbola ,x^2/a^2-y^2/b^2=1 whose centre i...

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  17. The asymptotes of a hyperbola are parallel to lines 2x+3y=0 and 3x+2y=...

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  18. If a hyperbola passing through the origin has 3x-4y-1=0 and 4x-3y-6=0 ...

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  19. The tangent at any point of a hyperbola 16x^(2) – 25y^(2) = 400 cuts o...

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