TS EAMCET · Maths · Circle
If the two circles \(x^2+y^2-2 x-6 y+10-r^2=0\) and \(x^2+y^2-8 x+2 y+8=0\) have a common chord of non-zero length, then
- A \(2 < r < 8\)
- B \(0 < r < 2\)
- C \(r=2,8\)
- D \(8 < r < 13\)
Answer & Solution
Correct Answer
(A) \(2 < r < 8\)
Step-by-step Solution
Detailed explanation
Let \(C_1=\) Centre of first circle \[ =\left[-\frac{1}{2} \times(-2),-\frac{1}{2} \times(-6)\right]=(1,3) \] \(C_2=\) Centre of second circle \[ =\left[-\frac{1}{2} \times(-8),-\frac{1}{2} \times(2)\right]=(4,-1) \] \(r_1=\) radius of first circle \(=\sqrt{1+9-10+r^2}=|r|\)…
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