Show that the lines joining the origin to the points common to x^2+hxy-y^2+gx+fy=0 And fx-gy=p are of right angle for all values of p.

Dear student

Please find the points of intersection be (x1,y1), (x2,y2)

now, from the origin the slopes can be obtained

be m1, m2

now, multiply m1 by m2 ie m1*m2

the product should be -1

Regards