TS EAMCET · Maths · Circle
If the circles \(x^2+y^2+2 k x-4 y+1=0\) and \(x^2+y^2-8 x-12 y+43=0\) touch each other then \(k=\)
- A 2
- B 1
- C -1
- D -2
Answer & Solution
Correct Answer
(C) -1
Step-by-step Solution
Detailed explanation
\( \text { } r_1=\sqrt{k^2+4-1} \Rightarrow \sqrt{k^2+3} \) and \(r_2=\sqrt{16+36-43}=\sqrt{52-43}=\sqrt{9}=3\) common tangent \(=S_1-S_2=0\) So, \(x^2+y^2+2 k x-4 y+1-x^2-y^2+8 x+12 y-43=0\) \( (2 k+8) x+8 y-42=0 \) Perpendicular drawn from any circle is equal to respective…
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