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`

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.

Statement 1 : The equations of the straight lines joining the origin to the points of intersection of x^2+y^2-4x-2y=4 and x^2+y^2-2x-4y-4=0 is x-y=0 . Statement 2 : y+x=0 is the common chord of x^2+y^2-4x-2y=4 and x^2+y^2-2x-4y-4=0

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 .

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

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 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 equation of a straight line joining the point of intersection of 3x+y+2=0 and x-2y-4=0 to the point of intersection of 7x-3y=-12 and 2y=x+3 .