TS EAMCET · Maths · Circle
If the angle between the circles \(x^2+y^2-4 x-6 y+k=0\) and \(x^2+y^2+8 x-4 y+11=0\) is \(\frac{\pi}{2}\), then the value of \(k\) is
- A \(-3\)
- B \(3\)
- C \(-15\)
- D \(15\)
Answer & Solution
Correct Answer
(D) \(15\)
Step-by-step Solution
Detailed explanation
Circles are orthogonal \(\begin{aligned} & \Rightarrow 2 g_1 g_2+2 f_1 f_2=\mathrm{C}_1+\mathrm{C}_2 \\ & \Rightarrow 2(-2)(4)+2(-3)(--2)=k+11 \\ & \Rightarrow-16+12=k+11 \Rightarrow k=-15\end{aligned}\)
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