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Let the circle x2+y2+4x+6y+λ=0(λ∈R)bisect the circumference of the circle x2+y2−2x+2y+(cos⁡ θ+sin⁡ θ)=0,(θ∈R) Then the product of maximum and minimum values of λ is

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answer is 2.

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Detailed Solution

Equation of common chord is 6x+4y+λ−cos⁡ θ−sin ⁡θ=0It passes through (1,-1).∴ 6−4+λ=cos ⁡θ+sin⁡ θ⇒ λ=cos⁡ θ+sin ⁡θ−2⇒ λmax=2−2 and λmin=−2−2⇒  Product =(2−2)(2+2)=2
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