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.

The length of normal at any point to the curve, y=c cosh(x/c) is

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.

A curve y=f(x) passes through the point P(1,1) . The normal to the curve at P is a(y-1)+(x-1)=0 . If the slope of the tangent at any point on the curve is proportional to the ordinate of the point. Determine the equation of the curve

A curve y=f(x) passes through point P(1,1) . The normal to the curve at P is a (y-1)+(x-1)=0 . If the slope of the tangent at any point on the curve is proportional to the ordinate of the point, then the equation of the curve is

A curve y=f(x) has the property that the perpendicular distance of the origin from the normal at any point P of the curve is equal to the distance of the point P from the x-axis. Then the differential equation of the curve

The portion of tangent to curve x=√a^2-y^2 +- a/2 log a-√a^2-y^2 intercepted between curve and x axis is of length

Find all the curves y=f(x) such that the length of tangent intercepted between the point of contact and the x-axis is unity.

Find the solpe of tangent at point (1, 1) of the curve x^(2)= y .

Find the point on the curve y=x^2-2x+3 , where the tangent is parallel to x-axis.