A normal is drawn at a point \( \mathrm{P}(\mathrm{x}, \mathrm{y}) ...

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A normal is drawn at a point \( \mathrm{P}(\mathrm{x}, \mathrm{y}) \) of a curve. It meets the \( \mathrm{x} \)-axis at Q. If \( \mathrm{PQ} \) is of constant length
\( \mathrm{P} \) \( \mathrm{k} \), then show that the differential equation describing such curves is, \( \mathrm{y} \frac{\mathrm{dy}}{\mathrm{dx}}=\pm \sqrt{\mathrm{k}^{2}-\mathrm{y}^{2}} \). Find the equation of such a curve passing through \( (0, \mathrm{k}) \).
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