The Points  $P(-3,-2)Q(9,10)$  and  $R(\alpha ,4)$  lies on a circle S with PR as its diameter. The tangents to S at the points Q and R intersect at the point T. If T lies on the line $4x-ky=2$  then k_____

Equation of a circle PR as diameter is  $(x+3)(x-\alpha )+(y-2)(y-4)=0$
   $Q(9,10)$   lies on it $\Rightarrow \alpha =13$ 
   Equation  $s=x^2+y^2-10x-6y-31=0$
Equation of tangent at Q and R is $S_1=0$  
     P.O.I =  $(\frac{25}{2},8)$   $\therefore 4\left(\frac{25}{2}\right)-k\left(8\right)=2 50-2=8k\Rightarrow k=6$