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Find the nature of the curve for which the length of the normal at any point P is equal to the radius vector.

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Find the nature of the curve for which the length of the normal at any point P is equal to the radius vector.

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The equation of the normal at P is 

x2 - y2 = c2,

which represents a rectangular hyperbola. Taking negative sign,

x2 + y2 = a2

which represents a circle.

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