The pole of a straight line with respect to the circle x2+y2=a2 lies on the circle x2+y2=9a2 If the straight - Maths - Conic Sections

Question

The pole of a straight line with respect to the circle x2+y2=a2
lies on the circle x2+y2=9a2 If the straight line touches the
circle x2+y2=r2 then a)9a2=r2 b)9r2=a2 c)r2=a2 d)3r2=a2 Answer is
(2) op[tion Plss explain it

Anuradha Sharma · Accepted Answer

Let the straight line be lx+my+n=0 1Let its pole be x1,y1 Its polar
wrt to the circle x2+y2=a2 2isxx1+yy1-a2=0 3But first and third
equation being same straight line , we have on comparing the
co-efficients, x1l=y1m=-a2nor x1=-la2n and y1=-mna2Since pole lies
on the circle x2+y2=9a2, we havel2a4+m2a4=9a2n2or a2l2+a2m2=9n2
4The line 1 will touch the circle x2+y2=9a2 if, nl2+m2=a3or if
a2l2+a2m2=9n2 which holds because of equation 4 Hence a2=9r2

The pole of a straight line with respect to the circle x2+y2=a2 lies on the circle x2+y2=9a2 If the straight line touches the circle x2+y2=r2 then a)9a2=r2 b)9r2=a2 c)r2=a2 d)3r2=a2 Answer is (2) op[tion Plss explain it.