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A circle whose diameter is major aixs of ellipe (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 (agtbgt0) meets axis at point P. Ifthe orthocentre of DeltaPF_(1)F_(2)lies on ellipse where F_(1)and F_(2) are foci of ellipse , then find the eccenricity of theellipse |
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Answer» Slope of altitude `S B,m_(1)=(b)/(ae)` Slope of `SA,m_(2)=(a)/(ae)` SINCE `m_(1)xxm_(2)=1`, we have `(b)/(be)((1)/(-e))=-1` `RARR 1-e^(2)=e^(4)` `rArre^(4)+e^(2)-1==0` `rArre^(2)=(sqrt(5)-1)/(2)` `rArre=sqrt((sqrt(5)-1)/(2))` |
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