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 angle between the line joining the points (1,-2) , (3,2) and the line x+2y -7 =0 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)

The minimum distance between a point on the curve y = e^x and a point on the curve y=log_e x is

Find the angle between the straight lines joining the origin to the point of intersection of 3x^2+5x y-3y^2+2x+3y=0 and 3x-2y=1

Find the equation of the bisectors of the angles between the lines joining the origin to the point of intersection of the straight line x-y=2 with the curve 5x^2+11 x y-8y^2+8x-4y+12=0

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

The angle between the lines joining origin to the points of intersection of the line sqrt(3)x+y=2 and the curve y^2-x^2=4 is (A) tan^(-1)(2/(sqrt(3))) (B) pi/6 (C) tan^(-1)((sqrt(3))/2) (D) pi/2

Find the maximum distance of any point on the curve x^2+2y^2+2x y=1 from the origin.

The curve in the first quadrant for which the normal at any point (x , y) and the line joining the origin to that point form an isosceles triangle with the x-axis as base is (a) an ellipse (b) a rectangular hyperbola (c) a circle (d) None of these

The distance between the origin and the tangent to the curve y=e^(2x)+x^2 drawn at the point x=0 is