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.