If the length of the portion of the normal intercepted between a curve and the x-axis varies as the square of the ordinate, find the equation of the curve.

If length of tangent at any point on the curve y=f(x) intercepted between the point and the x-axis is of length 1 . Find the equation of the curve.

lf length of tangent at any point on th curve y=f(x) intercepted between the point and the x-axis is of length 1. Find the equation of the curve.

Find the equation of the curve in which the subnormal varies as the square of the ordinate.

Find the equation of the curve in which the subnormal varies as the square of the ordinate.

The locus of the midpoints of the portion of the normal to the parabola y^(2)=16x intercepted between the curve and the axis is another parabola whose latus rectum is ___________ .

The area between the curve y=2x^(4)-x^(2) , the x-axis, and the ordinates of the two minima of the curve is

Find the curve for which the intercept cut off by any tangent on y-axis is proportional to the square of the ordinate of the point of tangency.

For the curve x y=c , prove that the portion of the tangent intercepted between the coordinate axes is bisected at the point of contact.

For the curve x y=c , prove that the portion of the tangent intercepted between the coordinate axes is bisected at the point of contact.

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)