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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Infinity Learn · Accepted Answer

$$r=$$ inradius of Δ$$OCF=1OF=6$$ and $$r=1$$⇒Δ$$=s12OF$$.$$OC=s$$⇒$$6b=2s(OC=b)(OF=ae=6)Perimeter$$ ofΔ$$OCF=2s$$⇒$$6+b+a=6b$$⇒$$5b=a+6$$⇒$$a2$$−$$a2e2=b2$$⇒$$b=52$$∴$$a=132$$;$$K=AB$$⋅$$CD=2a$$⋅$$2b$$[K]$$=$$[$$65$$]$$=8$$

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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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