A coplanar beam of light emerging from a point source have the equation \( \lambda x-y+2(1+\lamb...

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A coplanar beam of light emerging from a point source have the equation \( \lambda x-y+2(1+\lambda)=0, \forall \lambda \in R \); the rays of the beam strike an elliptical surface and get reflected inside the ellipse. The reflected rays form another convergent beam having the equation \( \mu x-y+2(1-\mu)=0, \forall \mu \in R \). Further it is found that the foot of the perpendicular from the point \( (2,2) \) upon any tangent to the ellipse lies on the circle \( x^{2}+y^{2}-4 y-5=0 \)
The area of the largest triangle that an incident ray and corresponding reflected ray can enclose with the major axis of the ellipse is equal to :
(a) \( 4 \sqrt{5} \)
(b) \( \sqrt{5} \)
(c) \( 3 \sqrt{5} \)
(d) \( 2 \sqrt{5} \)
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