Question

Let the equation of a circle be $x^2+y^2=a^2$ lf $h^2+k^2-a^2<0$, then the line $hx+ky=a^2$ is the

• A. polar line of the point (h.k) w.r.t. the circle.
• B. real chord of contact of the tangents from (h,k) to the circle.
• C. equation of a tangent to the circle from the point (h,k).
• D. midpoint chord of the circle which is bisected at (h,k).

Answer 1

The correct option is A polar line of the point (h.k) w.r.t. the circle.

Let P $(h,k)$ is a pole of line AB
$\therefore h^2+y^2-a^2<0$, which means it lies inside the circle
Therefore, real chord of contact of the tangents is not possible from $(h,k)$ and also tangents to the circle are also not possible.
If $(h,k)$ is mid point of any chord then equation is given by $hx+ky=h^2+k^2$
Given that $(h,k)$ is pole then equation of polar is given by
$\Rightarrow xh+yk-a^2=0$
So, AB is a polar line of the point $(h,k)$ w.r.t. the circle
Hence, option 'A' is correct.