Question

Abcd is a rectangle.the line through c perpendicular to ac meets ab produces at x and ad produced to y .prove that the points d,b,x,y are concyclic

Answer 1

am facing trouble with the following question

What is the condition that the two conic sections ax
2
1
+2h1xy+b1y2+2g1x+2f1y+c1=0 and ax
2
2
+2h2xy+b2y2+2g2x+2f2y+c2=0 intersects each other in four concyclic points.

I took the four points as unknown terms and since the points satisfies both the equations,I tried to put the points in each of the equations and tried to solve for the coordinates but it became useless and I got nothing.

Is there some way to arrive at the condition for the concyclicity of the intersecting points?Any help would be appreciated.Thanks