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AP EAMCET · Maths · Circle

If the point of contact of the circles \(x^2+y^2-6 x-4 y+9=0\) and \(x^2+y^2+2 x+2 y-7=0\) is \((\alpha, \beta)\), then \(7 \beta=\)

  1. A \(5 \alpha\)
  2. B \(2 \alpha\)
  3. C \(3 \alpha\)
  4. D \(4 \alpha\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(4 \alpha\)

Step-by-step Solution

Detailed explanation

Common chord: \((x^2+y^2-6x-4y+9)-(x^2+y^2+2x+2y-7)=0\) \(-8x-6y+16=0 \Rightarrow 4x+3y-8=0\) From \(4x+3y-8=0\), \(y = \frac{8-4x}{3}\). Substitute into \(x^2+y^2-6x-4y+9=0\): \(x^2 + \left(\frac{8-4x}{3}\right)^2 - 6x - 4\left(\frac{8-4x}{3}\right) + 9 = 0\)…