COMEDK · Maths · 12. Circle
If two circles \((x-1)^2+(y-3)^2=r^2\) and \(x^2+y^2-8 x+2 y+8=0\) intersect in two distinct points, then
- A \(2 < r < 8\)
- B \(r < 2\)
- C \(r=2\)
- D \(r>2\)
Answer & Solution
Correct Answer
(A) \(2 < r < 8\)
Step-by-step Solution
Detailed explanation
The first circle is \((x-1)^2 + (y-3)^2 = r^2\), which has center \(C_1 = (1, 3)\) and radius \(r_1 = r\). The second circle is \(x^2 + y^2 - 8x + 2y + 8 = 0\). Completing the square: \((x^2 - 8x + 16) + (y^2 + 2y + 1) = -8 + 16 + 1\), which simplifies to…
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