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Tangent drawn at any point P on a curve ...

Tangent drawn at any point P on a curve meets x-axis at Q such that circumcentre of `Delta POQ` has abscissa half that of ordinate. The differential equation to such a curve is

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The slope of the tangent at any arbitrary point of a curve is twice the product of the abscissa and square of the ordinate of the point. Then, the equation of the curve is (where c is an arbitrary constant)