Question

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

• A. polar lines of the points $(h,k)$ with respect to 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. none of these

Answer 1

The correct option is A polar lines of the points $(h,k)$ with respect to the circle

Let $(h,k)$ be any point
Then polar of $(h,k)$ with respect to $x^2+y^2=a^2$ is $hx+ky-a^2-0$
which is also a chord of contact of tangents fro point $(h,k)$