JEE Mains · Maths · STD 11 - 10.1 circle and system of circle
If the circles \((x+1)^2+(y+2)^2=r^2\) and \(x^2+y^2-4 x-4 y+4=0\) intersect at exactly two distinct points, then
- A \(5<\) r \(<9\)
- B \(0<\) r \(<7\)
- C \(3<\) r \(<7\)
- D \(\frac{1}{2}<\) r \(<7\)
Answer & Solution
Correct Answer
(C) \(3<\) r \(<7\)
Step-by-step Solution
Detailed explanation
If two circles intersect at two distinct points \(\Rightarrow\left|\mathrm{r}_1-\mathrm{r}_2\right|<\mathrm{C}_1 \mathrm{C}_2<\mathrm{r}_1+\mathrm{r}_2\) \( |\mathrm{r}-2|<\sqrt{9+16}<\mathrm{r}+2 \) \( |\mathrm{r}-2|<5 \text { and } \mathrm{r}+2>5\) \( -5<\mathrm{r}-2<5\)…
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