Comprehension- I A coplanar beam of light emerging from a point source have equation `lambda x-y+2(1+lambda)=0,lambda in R.` The rays of the beam strike an elliptical surface and get reflected. The reflected rays form another convergent beam having equation `mu x-y+2(1-mu)=0,mu in R.` Foot of the perpendicular from the point (2, 2) upon any tangent to the ellipse lies on the circle `x^2 + y^2 - 4y - 5 = 0` The eccentricity of the ellipse is equal toA. `1//3`B. `1//sqrt(3)`C. `2//3`D. none of these

Comprehension- I A coplanar beam of light emerging from a point source

1.	Comprehension- I A coplanar beam of light emerging from a point source have equation `lambda x-y+2(1+lambda)=0,lambda in R.` The rays of the beam strike an elliptical surface and get reflected. The reflected rays form another convergent beam having equation `mu x-y+2(1-mu)=0,mu in R.` Foot of the perpendicular from the point (2, 2) upon any tangent to the ellipse lies on the circle `x^2 + y^2 - 4y - 5 = 0` The eccentricity of the ellipse is equal toA. `1//3`B. `1//sqrt(3)`C. `2//3`D. none of these
Answer» `lambdax-y+2(1+lambda)=0` or `lambda(x+2)-(y-2)=0,lambda in R` This line passes through `(-2,2)` `mux-y+2(1-mu)=0, mu in R` or `mu(x-2)-(y-2)=0` This line passes through (2,2) Clearly, (-2,2) and (2,2) reprsente the foci of the ellipse So, 2ae=4 The circle `x^(2)+y^(2)-4y-5=0i.e.,x^(2)+(y-2)^(2)=9` respresent an auxiliar circle. Thus, `a^(2)=9 or e=2//3 and b^(2)=5`

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