AP EAMCET · Maths · Circle
If a direct common tangent drawn to the circles \(x^2+y^2\) \(6 x+4 y+9=0\) and \(x^2+y^2+2 x-2 y+1=0\) touches the circles at A and B , then \(\mathrm{AB}=\)
- A 9
- B 16
- C \(4 \sqrt{6}\)
- D \(2 \sqrt{6}\)
Answer & Solution
Correct Answer
(D) \(2 \sqrt{6}\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \text { } x^2+y^2-6 x+4 y+9=0 \\ & \Rightarrow(x-3)^2+(y+4)^2=4 ...(i)\\ & \text { and } x^2+y^2+2 x-2 y+1=0 \\ & \Rightarrow(x+1)^2+(y-1)^2=1 ...(ii)\\ & C_1=(3,-4), C_2=(-1,1), r_1=2, r_2=1 \end{aligned}\) So,…
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