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Prove that the portion of the tangent of...

Prove that the portion of the tangent of the rectangular hyperbola intercepted between the asymptotes is bisected at the point of contact and the area of the triangle formed by the tangent and the two asymptotes is constant.

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AAKASH SERIES-HYPERBOLA-Additional Exercise
  1. The equation of the line passing throught the centre of a rectangular ...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  16. If the normal at (x(i) y(i)) i=1,2,3,4 on xy=c^2 meet at the point (al...

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  17. Given the base BC of the triangle ABC and if angleC-angleB=k, a consta...

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  18. The ordinate of any point P on the hyperbola 25x^(2)-16y^(2)=400 is pr...

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  19. Given the base of the triangle and the sum of tangent of base angles a...

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  20. From a fixed point A(x(1),y(1)) a variable straight line is drawn to c...

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