AP EAMCET · Maths · Circle
If the angle between the circles \(x^2+y^2-4 x-6 y-3=0, x^2+y^2+8 x-4 y+\lambda=0\) is \(60^{\circ}\), then a value of \(\lambda\) is
- A \(-11\)
- B \(29\)
- C \(18\)
- D \(-29\)
Answer & Solution
Correct Answer
(D) \(-29\)
Step-by-step Solution
Detailed explanation
\(C_1=(2,3), r_1=\sqrt{(-2)^2+(-3)^2-(-3)}=\sqrt{16}=4\) \(C_2=(-4,2), r_2=\sqrt{4^2+(-2)^2-\lambda}=\sqrt{20-\lambda}\) \(d=\sqrt{(-4-2)^2+(2-3)^2}=\sqrt{36+1}=\sqrt{37}\) \(\cos\theta = \frac{r_1^2+r_2^2-d^2}{2r_1r_2}\)…
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