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Find the curve for which the sum of the ...

Find the curve for which the sum of the lengths of the tangent and subtangent at any of its point is proportional to the product of the co-ordinates of the point of tangency, the proportionality factor is equal to k.

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The correct Answer is:
`y = 1/k ln |c(k^2x^2-1)|`
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MOTION-DIFFERENTIAL EQUATION -Exercise 3
  1. A tank consists of 50 litres of fresh water. Two litres of brine each ...

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  2. A normal is drawn at a point P(x , y) of a curve. It meets the x-ax...

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  3. Find the curve for which the sum of the lengths of the tangent and sub...

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  4. Find the curve y= f(x) where f(X) ge 0, f(0) =0,bounding a curvilinear...

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  5. Find the equation of a curve such that the projection of its ordinate ...

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  6. The light rays emanating from a point source situated at origin when r...

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  7. The perpendicular from the origin to the tangent at any point on a cur...

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  8. Find the curve for which any tangent intersects the y-axis at the poin...

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  9. Find the curve such that the area of the trapezium formed by the co-or...

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  10. Find the equation of the curve passing through the origin if the middl...

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  11. A perpendicular drawn from any point P of the curve on the x-axis meet...

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  12. The equation of curve in which portion of y-axis cutoff between origin...

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  13. Find the orthogonal trajectories for the given family of curves when ‘...

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  14. The population P of a town decreases at a rate proportional to the num...

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  15. It is known that the decay rate of radium is directly proportional to ...

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  16. Let the function ln f(x) is defined where f(x) exists for x geq 2 an...

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  17. Find the differentiable function which satisfies the equation f(x)= -i...

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  18. Find all functions f(x) defined on (-pi/2,pi/2) with real values and h...

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  19. A tank contains 100 litres of fresh water. A solution containing 1 gm/...

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  20. A tank with a capacity of 1000 litres originally contains 100 gms of s...

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