The angle between the tangents at any point P and the line joining P to the origin O is the same...

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

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))=k tan^(-1)((y)/(x))

The tangents to a curve at a point on it is perpendicular to the line joining the point with the origin. Find the equation of the curve.

The tangents to a curve at a point on it is perpendicular to the line joining the point with the origin. Find the equation of the curve.

The equation of the curve lying in the first quadrant, such that the portion of the x - axis cut - off between the origin and the tangent at any point P is equal to the ordinate of P, is (where, c is an arbitrary constant)

If the angle between two tangents drawn from an external point P to a circle of radius 'a' and center O , is 60^(@), then find the length of OP.