Question

The distance between the chords of contact of the tangents to the circle $x^2+y^2+32x+24y-1=0$ from the origin and the point $(16,12)$ is $k$. The value of 40$k$ + 2350 is

Answer 1

Chord of contact from origin to the circle $x^2+y^2+32x+24y-1=0$
is given by $T=0\Rightarrow x\left(0\right)+y\left(0\right)+16(x+0)+12(y+0)-1=0\Rightarrow 16x+12y-1=0$
Thus distance of point $(16,12)$ from this line is, $=\left|\frac{16\times 16+12\times 12-1}{\sqrt{{16}^2+{12}^2}}\right|=\frac{399}{20}$
$\therefore 40k+2350=2\times 399+2350=3148$