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If the circles x2 + y2 + 2ax + cy + a = 0 and x2 + y2 – 3ax + dy – 1 = 0 intersect in two distinct points P and Q then the line 5x + by – a = 0 passes through P and Q for ?

If the circles x2 + y2 + 2ax + cy + a = 0 and x2 + y2 – 3ax + dy – 1 = 0 intersect in two distinct points P and Q then the line 5x + by – a = 0 passes through P and Q for ?

Grade:12

1 Answers

SHAIK AASIF AHAMED
askIITians Faculty 74 Points
8 years ago
Hello student,
Line equation of PQ is 5ax+(c-d)y+a+1=0
Also given that the line equation of PQ is
5x+by-a=0
so (5a/5=(c-d)/b=(a+1)/(-a)
As(a+1)/(-a)=a so a2+a+1=0
so line passes through for no value of a as its discriminant is <0
Thanks and Regards
Shaik Aasif
askIITians faculty

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