10 If the two conics a1x2+2h1xy+b1y2=c1, a2x2+2h2xy+b2y2=c2 intersect in 4 concyclic points, then a a1-b1h2=a2-b2h1 - Maths - Conic Sections

Question

10 If the two conics a 1 x 2 + 2 h 1 x y + b 1 y 2 = c 1 ,   a
2 x 2 + 2 h 2 x y + b 2 y 2 = c 2 intersect in 4 concyclic points,
then
a     a 1 - b 1 h 2 = a 2 - b 2 h 1      
              b     a
1 - b 1 h 1 = a 2 - b 2 h 2 c     a 1 + b 1 h 2 = a 2 + b
2 h 1                
    d     a 1 + b 1 h 1 = a 2 + b 2 h 2

Chat_5 · Accepted Answer

10. If the two conics a 1 x 2 + 2 h 1 x y + b 1 y 2 = c 1 , a 2 x 2 + 2 h 2 x y + b 2 y 2 = c 2 intersect in 4 concyclic points, then a . a 1 - b 1 h 2 = a 2 - b 2 h 1 b . a 1 - b 1 h 1 = a 2 - b 2 h 2 c . a 1 + b 1 h 2 = a 2 + b 2 h 1 d . a 1 + b 1 h 1 = a 2 + b 2 h 2