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`

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

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 .

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.

The equation of the line passing through the points of intersection of the circles 3x^2 +3y^2-2x + 12y-9=0 and x^2+y^2+6x+2y-15=0 is

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

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

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

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)