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Point “O” is the centre of an ellipse with major axis AB and minor axis CD. Point F is one focus of the ellipse. If OF = 6 and the diameter of the inscribed circle of the triangle OCF is 2 and the product of (AB)(CD) is k. Then the value of[k]=______. Where [.] denotes greatest integer function

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detailed solution

8

r= inradius of ΔOCF=1OF=6 and r=1Δ=s12OF.OC=s6b=2s(OC=b)(OF=ae=6)

Perimeter ofΔOCF=2s6+b+a=6b
5b=a+6a2a2e2=b2b=52a=132;K=ABCD=2a2b[K]=[65]=8

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