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.

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

The tangent at a point 'P' of a curve meets the axis of 'y' in N, the parallel through 'P' to the axis of 'y' meets the axis of X at M, O is the origin of the area of Delta MON is constant then the curve is (A) circle C) ellipse (D) hyperbola (B) parabola

The tangent at a point 'P' of a curve meets the axis of 'y' in N, the parallel through 'P' to the axis of 'y' meets the axis of X at M, O is the origin of the area of Delta MON is constant then the curve is (A) circle C) ellipse (D) hyperbola (B) parabola

The tangent at a point P of a curve meets the y-axis at A, and the line parallel to y-axis at A, and the line parallel to y-axis through P meets the x-axis at B. If area of DeltaOAB is constant (O being the origin), Then the curve is

The tangent at any point P on y^2 = 4x meets x-axis at Q, then locus of mid point of PQ will be

The curve is such that the length of the perpendicular from the origin on the tangent at any point P of the curve is equal to the abscissa of Pdot Prove that the differential equation of the curve is y^2-2x y(dy)/(dx)-x^2=0, and hence find the curve.

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__________

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__________

Find the eqution of the curve passing through the point (1,1), if the tangent drawn at any point P(x,y) on the curve meets the coordinate axes at A and B such that P is the mid point of AB.

The slope of the tangent any point on a curve is lambda times the slope of the joining the point of contact to the origin. Formulate the differential equation and hence find the equation of the curve.