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The eccentricity of the hyperbola `(x^(2))/(a^(2))-(y^(2))/(b^(2))=1` be reciprocal to that of the ellipse `x^(2)+4y^(2)=4`. If the hyperbola passes through a focus of the ellipse, then :A. The equation of the hyperbola is `(x^(2))/(3)-(y^(2))/(2)=1`B. a focus of the hyperbola is `(sqrt(3),0)`C. the eccentricity of the hyperbola is `sqrt((5)/(3))`D. the equation of the hyperbola is `x^(2)-3y^(2)=3` |
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Answer» Correct Answer - D Eccentricity of the ellipse `=sqrt(1-(1)/(4))=(sqrt(3))/(2)` Focus of the ellipse `=(-sqrt(3),0)` Eccentricity of the hyperbola `=sqrt(1+(b^(2))/(a^(2)))=(2)/(sqrt(3))implies(b)/(a)=(1)/(sqrt(3))` Since the hyperbola passes through the focus of the ellipse `(3)/(a^(2))-0=1impliesa^(2)=3` and `b^(2)=1` and equation of the hyperbola is `(x^(2))/(3)-(y^(2))/(1)=1` or `x^(2)-3y^(2)=3` Focus of hyperbola is `(pm 2,0)` |
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