List-I		List-II
(P)	If the straight lines $y=a_{1}x+b_1$ and $y=a_{2}x+b_2$,  $(a_1\ne a_2)$ and  $b_1\ne b_2$ meet the coordinate axes in concyclic points, then	(1)	$a_1^2+a_2^2=1$
(Q)	If the chord of contact of the tangents drawn to  $x^2+y^2=4$ from any point on  $x^2+y^2=a_1^2$ touches the circle  $x^2+y^2=a_2^2,(a_1\ne a_2)$, $(a_1,a_2>0)$, then	(2)	$a_1+a_2=20$
(R)	If the circles  $x^2+y^2+2a_{1}x+2a_{2}y-1=0$ and  $x^2+y^2-2a_{1}x-2a_{2}y-1=0$,  $(a_1\ne a_2)$ cut orthogonally, then	(3)	$a_1{a}_2=4$
(S)	If the shortest and largest distance from the point  $(8,5)$ to the circle $x^2+y^2-4x+6y-12=0$ are $a_1$ and $a_2$ respectively, then	(4)	$a_1{a}_2=1$

(P) Equation of any curve through the points in which given lines meet coordinate axes will be  $(a_{1}x-y+b)(a_{2}x-y+b)+\lambda xy=0$. If these points are concyclic then   $a_1{a}_2=1$
(Q) Any point on  $x^2+y^2=a_1^2$ will be  $(a_1\cos \theta ,a_1\sin \theta )$. The chord of contact of the tangents drawn to  $x^2+y^2=4$ from this point will be  $a_{1}x\cos \theta +a_{1}y\sin \theta =4$.
If this touches the circle  $x^2+y^2=a_2^2$, then  $a_1{a}_2=4$.
(R) If the two circles cut orthogonally, then  $2(-a_1\times a_1-a_2\times a_2)=(-1-1) \Rightarrow a_1^2+a_2^2=1$
(S) Centre of the given circle is  $(2,-3)$ & radius is 5. Now distance between  $(8,5)$ & the centre is 10. Hence $a_1=5\&a_2=15$