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Q.

A set of lines x+y-2+λ(2x+y-3)=0 represent incident rays on an ellipse s=0 and 2x+3y-23+μ(2x+y-3)=0 represent the set of reflective rays from the  same ellipse S=0,(λ,μ∈ℝ) . If P(3,7) is a point on S=0 and if the eccentricity of  the ellipse is A-B(A,B∈N) G.C.D (A,B)=1 then A-B equals

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answer is 9.

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Detailed Solution

The foci of the ellipse are points of intersections of family of lines givenS1,1,S'−72,10The eccentricity of the ellipse is ee=SS'SP+S'P=12405210+12405=41−3241−32=9
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