AP EAMCET · Maths · Circle
The slope of the common tangent drawn to the circles \(x^2+y^2-4 x+12 y-216=0\) and \(x^2+y^2+6 x-12 y+36=0\) is
- A \(1\)
- B \(-1\)
- C \(\frac{5}{12}\)
- D \(\frac{12}{7}\)
Answer & Solution
Correct Answer
(C) \(\frac{5}{12}\)
Step-by-step Solution
Detailed explanation
\(C_1=(2,-6), r_1=16\) \(C_2=(-3,6), r_2=3\) Let the common tangent be \(y=mx+c \Rightarrow mx-y+c=0\). \(|2m+6+c|=16\sqrt{m^2+1}\) \(|-3m-6+c|=3\sqrt{m^2+1}\) For direct common tangent: \(\frac{2m+6+c}{16} = \frac{-3m-6+c}{3}\) \(3(2m+6+c) = 16(-3m-6+c)\)…
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