JEE Main 2020 (Online) 9th January Evening ShiftQuestion 1
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 ________.
Circle
Answer$36$
Solution
Circles: centre $(3,0)$, $r=1$; and $x^2+(y-4)^2=k$, centre $(0,4)$, radius $\sqrt k$. Distance between centres is $5$. External touch: $\sqrt k+1=5\Rightarrow k=16$. Internal touch: $\sqrt k-1=5\Rightarrow k=36$. Largest $k=36$.