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 tangents to the curves y=sin x and y = cos x at their point of intersection is

The angle between the lines joining the origin to the points of intersection of the line sqrt3x+y=2 and the curve y^(2)-x^(2)=4 is

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)

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

The angle between the tangents to the curves y=x^(2)andx=y^(2) at (1,1) is -

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 (a) ( b ) (c) y=( d ) e^(( e ) (f) K(( g ) (h) x-1( i ))( j ))( k ) (l) (m) (b) ( n ) (o) y=( p ) e^(( q ) (r) K e (s))( t ) (u) (v) (c) ( d ) (e) y=( f ) e^(( g ) (h) K(( i ) (j) x-2( k ))( l ))( m ) (n) (o) (d) None of these

A curve y=f(x) passes through the 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, 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) .