Let C1 and C2 be two circles whose equations are given as x2+y2=25 and x2+y2+10x+6y+1=0. C3 is a variable circle which cuts C1 and C2 orthogonally. Tangents are drawn from centre of C3 to C1. If the locus of mid-point of chord of contact of tangents is αx+3y+13β(x2+y2)=0, then the value of βα is

Let C1 and C2 be two circles whose equations are given as x2+y2=25 and

1.	Let C1 and C2 be two circles whose equations are given as x2+y2=25 and x2+y2+10x+6y+1=0. C3 is a variable circle which cuts C1 and C2 orthogonally. Tangents are drawn from centre of C3 to C1. If the locus of mid-point of chord of contact of tangents is αx+3y+13β(x2+y2)=0, then the value of βα is
Answer» Let $C_{1}$ and $C_{2}$ be two circles whose equations are given as $x^{2} + y^{2} = 25$ and $x^{2} + y^{2} + 10 x + 6 y + 1 = 0.$ $C_{3}$ is a variable circle which cuts $C_{1}$ and $C_{2}$ orthogonally. Tangents are drawn from centre of $C_{3}$ to $C_{1}$ . If the locus of mid-point of chord of contact of tangents is $α x + 3 y + \frac{13}{β} (x^{2} + y^{2}) = 0$ , then the value of $\frac{β}{α}$ is