What is the condition for 2 conic to intersect at 4 concyclic points?
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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
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
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