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

If 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 the subtangent at any point on the curve y=be^(x/3) is

The length of tangent at a point P(x_(1),y_(1)) to the curve y=f(x) ,having slope m at P is

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

If the tangent at any point on the curve y=x^(5)+5x-12 makes an angle theta with the x - axis then theta is

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. Also obtain the area bounded by the y-axis, the curve and the normal to the curve at P .

The points on the curve y=sin x ,where the tangent is parallel to the x axis 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

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