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A normal is drawn at a point `P(x , y)` of a curve. It meets the x-axis at `Qdot` If `P Q` has constant length `k ,` then show that the differential equation describing such curves is `y(dy)/(dx)=+-sqrt(k^2-y^2)` . Find the equation of such a curve passing through `(0, k)dot`

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The correct Answer is:
`x^2 +y^2 = k^2`
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MOTION-DIFFERENTIAL EQUATION -Exercise 3
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  2. A tank consists of 50 litres of fresh water. Two litres of brine each ...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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