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 line of the point $$\left( {h,\,k} \right)$$ with respect to the circle
B.
real chord of contact of the tangents from $$\left( {h,\,k} \right)$$ to the circle
C.
equation of a tangent to the circle from the point $$\left( {h,\,k} \right)$$
D.
none of these
Answer :
polar line of the point $$\left( {h,\,k} \right)$$ with respect to the circle
Solution :
$$\left( {h,\,k} \right)$$ is a point in the interior of the circle $${x^2} + {y^2} = {a^2}.$$ So, $$hx + ky = {a^2}$$ neither can be a real tangent nor a chord of contact of tangents.