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Let the foci of the hyperbola (X^(2))/(A^(2))-(y^(2))/(B^(2))=1 be the vertices of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 and the foci of the ellipse be the vertices of the hyperbola. Let the eccentricities of the ellipse and hyperbola be e_(E) and e_(H), respectively. Then match the following lists. |
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Answer» `A=ae_(E) and a=Ae_(H)` `"or"e_(E)e_(H)=1` `therefore""e_(E)+e_(H)gt2""("Using "e_(E)+e_(H)gtsqrt(e_(E)e_(H)))` `B^(2)=A^(2)(e_(H)^(2)-1)=a^(2)(1-e_(E)^(2))=b^(2)` `"or"(b)/(B)=1` Also, the angle between the asymptotes is `2TAN^(-1).(B)/(A)=(2pi)/(3)` Also, `(B)/(A)=sqrt3or(b)/(ae_(E))=sqrt3ore_(E)^(2)=(1)/(4)` Solving `(X^(2))/(a^(2))+(y^(2))/(b^(2))=1 and (x^(2))/(a^(2)e_(E)^(2))-(y^(2))/(b^(2))=1 or(2X^(2))/(a^(2))-(y^(2))/(b^(2))=1` Now, solve. |
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