A) Exactly one value of a
B) No value of a
C) Infinitely many values of a
D) Exactly two values of a
Correct Answer: B
Solution :
[b] \[{{S}_{1}}={{x}^{2}}+{{y}^{2}}+2ax+cy+a=0\] \[{{S}_{2}}={{x}^{2}}+{{y}^{2}}-3ax+dy-1=0\] Equation of common chord of circles \[{{S}_{1}}\] and \[{{S}_{2}}\]is given by \[{{S}_{1}}-{{S}_{2}}=0\] \[\Rightarrow 5ax+(c-d)y+a+1=0\] Given that \[5x+by-a=0\] passes through P and Q \[\therefore \] The two equation should represent the same line \[\Rightarrow \frac{a}{1}=\frac{c-d}{b}=\frac{a+1}{-a}\Rightarrow a+1=-{{a}^{2}}\] \[\Rightarrow {{a}^{2}}+a+1=0\] No real value of a.
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