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res_saj

Does AIEEE exams really follow the syllabus they have given in their website?
I recently did a question from the AIEEE 2005

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
(1) exactly one value of a (2) no value of a
(3) infinitely many values of a (4) exactly two values of a

Solution : (2)
S1 = x2 + y2 + 2ax + cy + a = 0
S2 = x2 + y2 - 3ax + dy - 1 = 0
Equation of radical axis of S1 and S2
S1 - S2 = 0
=> 5ax + (c - d)y + a + 1 = 0
Given that 5x + by - a = 0 passes through P and Q
a/1 = c-d/b = a+1/-a
=> a + 1 = -a2
a2 + a + 1 = 0
No real value of a.

Radical axis is not mentioned in the syllabus, n.. and I'm even hearing that word for the first time. Even if there is any alternate method - it'll be obviously longer than this -- for we get only 1 minute per question.

Does anyone know what exactly is the syllabus for the AIEEE?

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