Jee Main 2024 30 01 2024 Shift1 - Question5
Question 5
The range of $r$ for which circles $(x+1)^{2}+(y+2)^{2}=$ $r^{2}$ and $x^{2}+y^{2}-4 x-4 y+4=0$ coincide at two distinct points
(1) $3<r<7$
(2) $5<r<9$
(3) $\frac{1}{2}<r<4$
(4) $0<r<3$
Show Answer
Answer: (1)
Solution:
If two circles intersect at two distinct points
$\Rightarrow\left|r _1-r _2\right|<C _1 C _2<r _1+r _2$
$|r-2|<\sqrt{9+16}<r+2$
$|r-2|<5 \quad$ and $r+2>5$
$-5<r-2<5 \quad r>3$
$-3<r<7$
From (1) and (2)
$3<r<7$
BETA
