Question

If the curves, $x^2-6x+y^2+8=0$ and $x^2-8y+y^2+16-k=0,(k>0)$ touch each other at a point, then the largest value of k is __________.
Given 859

Answer 1

Answer: 36.00

Common tangent is $S_1-S_2=0$
$\Rightarrow -6x+8y-8+k=0$
Use $p=r$ for $I^{st}$ circle
$\Rightarrow \frac{|-18-8+k|}{10}=1$
$\Rightarrow k=36$ or $16\Rightarrow k_{max}=36$