JEE PYQ: Circle Question 23
Question 23 - 2020 (09 Jan Shift 2)
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 ______.
Show Answer
Answer: 36
Solution
Circle 1: $(x-3)^2 + y^2 = 1$, center $(3,0)$, $r_1 = 1$. Circle 2: $x^2 + (y-4)^2 = k$, center $(0,4)$, $r_2 = \sqrt{k}$. Distance $= 5$. Touch: $\sqrt{k} + 1 = 5$ or $|\sqrt{k} - 1| = 5$. Max $k$: $\sqrt{k} = 6 \Rightarrow k = 36$.
BETA
