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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

  1. A \(2 < r < 8\)
  2. B \(0 < r < 2\)
  3. C \(r=2,8\)
  4. D \(8 < r < 13\)
Verified Solution

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 \(=\sqrt{1+9-10+r^2}=|r|\)…