If the circles x^2+y^2+2 a x+c y+a=0 and x^2+y^2-3 a x+d y-1=0 intersect in two distinct points P and Q then the line 5 x+ by -a=0 passes through P and Q for

Step-by-step solution

aligned & S₁=x^2+y^2+2 a x+c y+a=0 & S₂=x^2+y^2-3 a x+d y-1=0 aligned Equation of radical axis of S₁ and S₂ aligned & S₁-S₂=0 & 5 a x+(c-d) y+a+1=0 aligned Given that 5 x + by - a =0 passes through P and Q aligned & a 1 = c-d b = a+1 -a & a+1=-a^2 & a^2+a+1=0 aligned No real value of a.