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TS EAMCET · Maths · Circle

If \(C_1\) and \(C_2\) are the centres of similitude with respect to the circles \(x^2+y^2-14 x+6 y+33=0\) and \(x^2+y^2+30 x-2 y+1=0\), then the equation of the circle with \(C_1 C_2\) as diameter is

  1. A \(2 x^2+2 y^2+30 x-33 y-17=0\)
  2. B \(2 x^2+2 y^2-14 x+9 y-13=0\)
  3. C \(2 x^2+2 y^2-39 x+14 y+74=0\)
  4. D \(2 x^2+2 y^2-24 x+8 y-5=0\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(2 x^2+2 y^2-39 x+14 y+74=0\)

Step-by-step Solution

Detailed explanation

Given equation of circles are \( x^2+y^2-14 x+6 y+33=0 \) and \( x^2+y^2+30 x-2 y+1=0 \) Clearly, circle (i) has centre \(O_1(7,-3)\) \( \text { and radius } r_1=\sqrt{49+9-33}=5 \) and circle (ii) has centre \(O_2(-15,1)\) and radius \(r_2=\sqrt{225+1-1}=15\) We know that the…