question_answer

If the circles\[{{x}^{2}}+{{y}^{2}}+2ax+cy+a=0\]and \[{{x}^{2}}+{{y}^{2}}-3\text{ }ax+dy-1=0\]intersect in two distinct points P and 0, then the line \[5x+by-a=0\]passes through P and Q for     AIEEE  Solved  Paper-2005

A) exactly two values of a

B) infinitely many values of a

C) no value of a

D) exactly one value of a

Correct Answer: C

Solution :

Ifandare tw0 circles, then the equation of line passes through the points of intersection ofandis Given equation of circles are andrespectively. Chord through intersection points P and 0 of the circlesand is             On comparing with we get which gives no real value of a. The line will passes through P and Q for no value of a.