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Show that the segment of the tangent to the hyperbola `y = frac{a^2}{x}` intercepted between the axes of the coordinates is bisected at the point of contact

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Prove that the segment of the tangent to the hyperbola y = (c )/(x) which is contained between the coordinate axes is bisected at the point of tangency.

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Prove that the segment of tangent to xy=c^(2) intercepted between the axes is bisected at the point at contact .

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A DAS GUPTA-Application of dy/dx-Exercise
  1. Show that the segment of the tangent to the curve y=a/2I n((a+sqrt(a^2...

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  2. If alpha, beta are the intercepts made on the axes by the tangent at a...

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  3. Show that the segment of the tangent to the hyperbola y = frac{a^2}{x}...

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  4. Find the value of n in N such that the curve (x/a)^n+(y/b)^n=2 touche...

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  5. Find the equation of the normal to the curve y=(1+y)^y+sin^(-1)(sin^2x...

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  6. Prove that the equation of the normal to x^(2/3)+y^(2/3)=a^(2/3) is yc...

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  7. Find the equation of the normal to the curve x^2=4ywhich passes throu...

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  8. Find the points on the curve 9y^2=x^3 where normal to the curve makes ...

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  9. Prove that all normals to the curve x=acost+a tsint ,\ \ y=asint-a ...

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  10. Show that for any point of the curve x^2 - y^2 = a^2 the segment of th...

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  11. Use calculus to find the conditiion that the line xcos theta + ysin th...

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  12. The volume of the cylindrical trunk of a tree is proportional to the c...

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  13. A stick of length 100 cm rests against a vertical walland the horizont...

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  14. A man running along a circular track has the speedof 10 km per hour. A...

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  15. A point is moving along the curve y^(3)=27x. The interval in which the...

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  16. A particle is moving along the parabola y^2 = 12x at the uniform rate ...

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  17. A spherical balloon is being inflated so that itsvolume increases unif...

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  18. The time t of a complete oscillation of a simple pendulum of length l ...

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  19. The time t of a complete oscillation of a simple pendulum of length l ...

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  20. A spherical iceball is melting, such that the radius is decreasing at ...

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