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 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

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 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 point of intersection of the circle x^2+y^2-3x-4y+2=0 with the x-axis.

Prove that the straight lines joining the origin to the point of intersection of the straight line h x+k y=2h k and the curve (x-k)^2+(y-h)^2=c^2 are perpendicular to each other if h^2+k^2=c^2dot

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

The point of intersection of the curves y^(2) = 4x and the line y = x is

Prove that the pair of straight lines joining the origin to the points of intersection of the circles x^2+y^2=a and x^2+y^2+2(gx+fy)=0 is a^(prime)(x^2+y^2)-4(gx+fy)^2=0

Prove that the straight lines joining the origin to the points of intersection of 3x^(2)+5xy-3y^(2)+2x+3y=0 " and " 3x-2y-1=0 are at right angles.

Show that straight lines joining the origin to the points of intersection of 3x-2y+2=0 and 3x^2+5x-2y^2+4x+5y=0 are at right angles .