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AP EAMCET · Maths · Circle

If the circles \(x^2+y^2-6 x-8 y-12=0\) and \(x^2+y^2-4 x+6 y+k=0\) are perpendicular to each other, then ' \(k\) ' equals

  1. A 4
  2. B 0
  3. C -2
  4. D 12
Verified Solution

Answer & Solution

Correct Answer

(B) 0

Step-by-step Solution

Detailed explanation

\[ \begin{aligned} & C_1: x^2+y^2-6 x-8 y-12=0 \\ & C_2: x^2+y^2-4 x+6 y+k=0 \end{aligned} \] Both the circles are perpendicular to each other. \[ \begin{aligned} \because \quad g_1 & =-3, f_1=-4, c_1=-12 \\ & g_2=-2, f_2=3, c_2=k \end{aligned} \] \(\because\) If two circles…