Question

The pole of the line $8x-2y=11$ w.r.t. to the circle $2x^2+2y^2=11$ is

• A. $(4,1)$
• B. $(4,-1)$
• C. $(3,1)$
• D. $(4,2)$

Answer 1

Answer: (B)

$(4,-1)$

Let, $p(h,k)$ is a pole of the line $8x-2y=11$ w.rt. the circle
$x^2+y^2=\frac{11}{2}$
then, from $p(h,k)$ chord of contact to circle is
$xh+yk-\frac{11}{2}=0$ -------(1)
$8x-2y=11$ -------(2)
equation (1) & equation(2) represent same line
$\frac{h}{8}=\frac{k}{-2}=\frac{11}{2\times 11}=\frac{1}{2}$
$h=4$ and $k=-1$
so, pole of line $8x-2y=11$ is $p(4,-1)$