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Question

If the circles x2+y2+2ax+cy+a=0andx2+y2−3ax+dy−1=0 interesect in two distinct points P andn Q then the line 5x + by - a = 0 passes through P and Q for
(2005)


A

exactly on value of a

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B

no value of a

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C

infinitely many values of

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D

exactly two value of a

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Solution

The correct option is B

no value of a


S1=x2+y2+2ax+cy+a=0
S2=x2+y23ax+dy1=0
Equation of radical axis of S1andS2
S1S2=05ax+(cd)y+a+1=0
Given that 5x + by - a = 0 passes through P and Q

a1=cdb=a+1aa+1=a2
a2+a+1=0 aR.
Not real value of a.


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