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TS EAMCET · Maths · Circle

If the circle \(x^2+y^2+8 x-4 y+c=0\) touches the circle \(x^2+y^2+2 x+4 y-11=0\) externally and cuts the circle \(x^2+y^2-6 x+8 y+k=0\) orthogonally, then \(k\) is equal to

  1. A 59
  2. B -59
  3. C 19
  4. D -19
Verified Solution

Answer & Solution

Correct Answer

(B) -59

Step-by-step Solution

Detailed explanation

Given that circle \(x^2+y^2+8 x-4 y+c=0\) touch the circle \(x^2+y^2+2 x+4 y-11=0\) then, \(C_1 C_2=r_1+r_2\) ...(i) where \(\begin{gathered} C_1=(-4,2) \\ r_1=\sqrt{16+4-c}=\sqrt{20-c} \\ C_2=(-1,-2) \end{gathered}\) and \(r_2=\sqrt{1+4+11}=4\) \(\therefore\) From Eq. (i),…