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A normal is drwn at a point P(x,y) of a ...

A normal is drwn at a point P(x,y) of a curve. It meets the x-axis at Q. If PQ is of 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).

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The correct Answer is:
`x^(2)+y^(2)=k^(2)`
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