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The family of curves in which the sub-ta...

The family of curves in which the sub-tangent at any point to any curve is double the abscissa is given by

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The perpendicular from the origin to the tangent at any point on a curve is equal to the abscissa of the point of contact. Also curve passes through the point (1,1). Then the length of intercept of the curve on the x-axis is__________