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Find the equation of the curve passing t...

Find the equation of the curve passing through the origin if the middle point of the segment of its normal from any point of the curve to the x-axis lies on the parabola `2y^2=x`

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The correct Answer is:
`y^2 = 2x +1 -e^2x`
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MOTION-DIFFERENTIAL EQUATION -Exercise 3
  1. Find the curve for which any tangent intersects the y-axis at the poin...

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

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

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

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

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

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

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

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

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

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

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

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

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  14. (dy)/(dx)=y+int0^1 ydx given y=1 where x=0

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  15. Find the continuous function which satisfies the relation, int0^x t f(...

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  16. A curve passing through (1, 0) such that the ratio of the square of th...

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  17. The curve f(x) is given by

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  18. The curve g(x) is given by -

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  19. The value of int1^2(g(x) -f(x))dx is-

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  20. {:( " Column - I" , " Column - II") , ( "(A) A curve passing through...

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