Show that the angle between the tangent at any point P and the line joining P to the origin O is same at all points on the curve `log(x^2+y^2)=ktan^(-1)(y/x)`

The length of subtangent at any point of the curve log y = 25x is

Prove that the angle between the lines joining the origin to the points of intersection of the straight line y=3x+2 with the curve x^2+2x y+3y^2+4x+8y-11=0 is tan^(-1)((2sqrt(2))/3)

Angle between the tangents to the curve y=x^2-5x+6 at the points (2,0) and (3,0) is

Find the equations of the straight lines joining the origin to the points of intersection of x^2+y^2-4x-2y=0 and x^2+y^2-2x-4y=4 .

A curve C has the property that if the tangent drawn at any point P on C meets the co-ordinate axis at A and B , then P is the mid-point of A Bdot The curve passes through the point (1,1). Determine the equation of the curve.

The line y = x + 1 is a tangent to the curve y^(2) = 4x at the poin

If the tangent at any point P of a curve meets the axis of x in T. Then the curve for which OP=PT,O being the origins is

Find the slope of the tangent to curve y=x^(3)-x+1 at the point whose x- coordinate is 2.

The lines joining the origin to the points of intersection of 2x^2 + 3xy -4x +1 = 0 and 3x + y=.1 given by

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).