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

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.

If slope of the tangent at the point (x, y) on the curve is (y-1)/(x^(2)+x) , then the equation of the curve passing through M(1, 0) is :

The slope of tangent at a point P(x, y) on a curve is - x/y . If the curve passes through the point (3, -4) , find the equation of the curve.

The slope of the tangent at a point P(x, y) on a curve is (- (y+3)/(x+2)) . If the curve passes through the origin, find the equation of the curve.

On the curve y=f(x) the length of tangent and length of subnormal at (x,y),y!=0, are equal,then square of slope of tangent will be

Point at which the tangent to the curve y=3x-2x^(2) has slope m=-1 is