Question

If the tangent are drawn from any point on the line $x+y=3$ to the circle $x^2+y^2=9$, then the chord of contact passes through the point $(k,k)$, where $k=$

Answer 1

The coordinate of nay point on the line $x+y=3$ are $(k,3-k)$.

The equation of chord of contact of tangents drawn from $(k,3-k)$ to the circle $x^2+y^2=9$ is

$k.x+(3-k).y=9\Rightarrow (3y-9)+k(x-y)=0$

which clearly passes through the intersection of

$(3y-9)=0$ and $x-y=0$ i.e. $(3,3)$

$\therefore k=3$