AP EAMCET · Maths · Circle
If the acute angle between the circles \(S \equiv x^2+y^2+2 k x+4 y-3=0\) and \(S^1 \equiv x^2+y^2-4 x+2 k y+9=0\) is \(\operatorname{Cos}^{-1}\left(\frac{3}{8}\right)\) and the centre of \(S^1=0\) lies in the first quadrant, then the radical axis of \(S=0\) and \(S^1=0\) is
- A \(x-5 y+6=0\)
- B \(x-5 y-4=0\)
- C \(5 x-y-6=0\)
- D \(5 x-y-4=0\)
Answer & Solution
Correct Answer
(A) \(x-5 y+6=0\)
Step-by-step Solution
Detailed explanation
\(C_1=(-k,-2), r_1^2=k^2+7\) \(C_2=(2,-k), r_2^2=k^2-5\) \(C_2\) in first quadrant \(\implies -k>0 \implies k0 \implies k^2>5\). \(d^2 = (2-(-k))^2 + (-k-(-2))^2 = (2+k)^2+(2-k)^2 = 4+4k+k^2+4-4k+k^2 = 8+2k^2\) \(\cos\theta = \frac{|r_1^2+r_2^2-d^2|}{2r_1r_2}\)…
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