The gradient of the tangent to the curve at a point is k times to the gradient of the straight line joining this pint and origin. Find the equation of the curve, where `k(ne0)` is constant.

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.

A curve having the condition that the slope of tangent at some point is two times the slope of the straight line joining the same point to the origin of coordinates is a//an -

The equation of the tangent to the curve y= be^(-(x)/(a)) at the point where it crosses the y-axis is-

A curve passes through the point (3,-4) and the slope of the tangent to the curve at any point (x,y) is (-(x)/(y)) . Find the equation of the curve.

The slope of the tangent to a curve at any point (x,y) is (3y+2x+4)/(4x+6y+5) . If the curve passes through (0,-1), find the equation of the curve.

Determine the constant c such that the straight line joining the points (0,3) and (5-2) is a tangent to the curve y=(c )/(x+1) .

At any point (x,y) of a curve, the slope of the tangent is twice the slope of the line segment joining the point of contact to the point(-4, -3).Find the equation of the curve given that it passes through (-2, 1).

Find the equation of the straight line which is tangent at one point and normal at another point of the curve x=3t^(2), y=2t^(3) .

2x-3y+5=0 in this given straight line find the gradient and y intercept.

The equation of the tangent to the curve y={(x^2sin"1/x,xne0),(0,x=0):} at the origin is