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 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'(x^(2)+y^(2))-4(gx+fy)^(2)=0

The lines joining the origin to the point of intersection of x^2+y^2+2gx+c=0 and x^2+y^2+2fy-c=0 are at right angles if

The lines joining the origin to the point of intersection of x^2+y^2+2gx+c=0 and x^2+y^2+2fy-c=0 are at right angles if

The lines joining the origin to the point of intersection of x^2+y^2+2gx+c=0 and x^2+y^2+2fy-c=0 are at right angles if

The lines joining the origin to the point of intersection of the curves x^(2)+y^(2)+2gx+c=0 and x^(2)+y^(2)+2fy-c=0 are at right angles if

The lines joining the origin to the points of intetsection of x^2+y^2+2gx+c=0 and x^2+y^2+2fy-c=0 are at right angle is

The angle between the lines joining the origin to the points of intersection of curve x^(2)+hxy-y^(2)+gx+fy=0 and fx-gy=k is

The lines joining the origin to the point of intersection of x^(2)+y^(2)+2gx+c=0 and x^(2)+y^(2)+2fy-c=0 are at right angles if

Show that the pair of lines joining the origin to the points of the intersection of the line fx-gy= lambda with the curve x^(2)+hxy-y^(2)gx+fy=0 are at right angles AA lambda in R .

The length of the common chord of the circles x^(2) + y^(2) + 2gx + c = 0 and x^(2) + y^(2) + 2fy - c = 0 is