TS EAMCET · Maths · Circle
If \(m_1\) and \(m_2\) are the slopes of the direct common tangents drawn to the circles \(x^2+y^2-2 x-8 y+8=0\) and \(x^2+y^2-8 x+15=0\), then \(m_1+m_2=\)
- A \(-\frac{24}{5}\)
- B \(\frac{12}{5}\)
- C \(\frac{24}{5}\)
- D \(-\frac{12}{5}\)
Answer & Solution
Correct Answer
(A) \(-\frac{24}{5}\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & P \equiv\left(\frac{12-1}{2}, \frac{0-4}{2}\right)=\left(\frac{11}{2},-2\right) \\ & \\ & \Rightarrow \frac{y+2}{x-\frac{11}{2}}=m \Rightarrow y+2=m\left(x-\frac{11}{2}\right) \\ & \Rightarrow y-m x+2+\frac{11 m}{2}=0 \\ & \\ & \Rightarrow\left|\frac{-4…
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