ExamBro
ExamBro
AP EAMCET · Maths · Circle

The equation of the circle which cuts the circles
\(\begin{aligned}
& S_1 \equiv x^2+y^2-4=0 \\
& S_2 \equiv x^2+y^2-6 x-8 y+10=0 \\
& S_3 \equiv x^2+y^2+2 x-4 y-2=0
\end{aligned}\)
at the extremities of diameters of these circles is

  1. A \(x^2+y^2-4 x-6 y-4=0\)
  2. B \(x^2+y^2+4 x-4=0\)
  3. C \(x^2+y^2=25\)
  4. D \(x^2+y^2+x+y+1=0\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(x^2+y^2-4 x-6 y-4=0\)

Step-by-step Solution

Detailed explanation

Let the equation of required circle is \(S \equiv x^2+y^2+2 g x+2 f y+c=0\) and equation of given circles \(\begin{aligned} & S_1 \equiv x^2+y^2-4=0 \\ & S_2 \equiv x^2+y^2-6 x-8 y+10=0 \\ & S_3=x^2+y^2+2 x-4 y-2=0 \end{aligned}\) \(\because\) Circle \(S=0\) cuts the circles…