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Show that the segment of the tangent to ...

Show that the segment of the tangent to the curve `y=a/2I n((a+sqrt(a^2-x^2))/(a-sqrt(a^2-x^2)))-sqrt(a^2-x^2)` contained between the y=axis and the point of tangency has a constant length.

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Show that the segment of the tangent to the curve y=(a)/(2)In((a+sqrt(a^(2)-x^(2)))/(a-sqrt(a^(2)-x^(2))))-sqrt(a^(2)-x^(2)) contained between the y= axis and the point of tangency has a constant length.

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A DAS GUPTA-Application of dy/dx-Exercise
  1. The sum of the intercepts made on the axes of coordinates by any tange...

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  2. Prove that the tangent at any point on the rectangular hyperbola xy = ...

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  3. Show that the segment of the tangent to the curve y=a/2I n((a+sqrt(a^2...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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