AP EAMCET · Maths · Circle
If the two circles \((x-1)^2+(y-3)^2=r^2\) and \(x^2+y^2-8 x+2 y+8=0\) intersect in two different points, then what can we conclude about \(r\) ?
- A \(r < 2\)
- B \(r=2\)
- C \(r>2\)
- D \(2 < r < 8\)
Answer & Solution
Correct Answer
(D) \(2 < r < 8\)
Step-by-step Solution
Detailed explanation
As circles intersects in two distinct points So, \(\left|r_1-r_2\right| < \left|C_1 C_2\right| < r_1+r_2\) ...(i) Here, \(\quad C_1=(1,3), C_2=(4,-1)\) \(\begin{aligned} \therefore \quad C_1 C_2 & =\sqrt{(4-1)^2+(-1-3)^2} \\ & =\sqrt{9+16}=5 \end{aligned}\)…
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