The tangent at any point `P` of a curve `C` meets the x-axis at `Q` whose abscissa is positive and `OP = OQ, O` being the origin, the equation of curve C satisfying these conditions may be

If the tangent at any point P of a curve meets the axis of X in T find the curve for which O P=P T ,O being the origin.

If the tangent at any point P of a curve meets the axis of XinTdot find the curve for which O P=P T ,O being the origin.

If the tangent at any point P of a curve meets the axis of x in T. Then the curve for which OP=PT,O being the origins is

If the tangent at any point P of a curve meets the axis of x in T. Then the curve for which OP=PT,O being the origins is

The ordinate and the normal at any point P on the curve meet the x-axis at points A and B respectively. Find the equation of the family of curves satisfying the condition , The product of abscissa of P and AB =arithmetic mean of the square of abscissa and ordinate of P .

The ordinate and the normal at any point P on the curve meet the x-axis at points A and B respectively. Find the equation of the family of curves satisfying the condition , The product of abscissa of P and AB =arithmetic mean of the square of abscissa and ordinate of P .

The perpendicular from the origin to the tangent at any point on a curve is equal to the abscissa of the point of contact. Find the equation of the curve satisfying the above condition and which passes through (1, 1).

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)