A hyperbola whose transverse axis is along the major axis of the conic,`x^2/3+y^2/4= 4` and has vertices atthe foci of this conic. If the eccentricity of the hyperbola is `3/2`, then which of the following points does NOT lie on it?A. `(sqrt(5),2sqrt(2))`B. `(sqrt(5),2sqrt(3))`C. `(0,2)`D. `(sqrt(10),2sqrt(3))`

A hyperbola whose transverse axis is along the major axis of the conic

1.	A hyperbola whose transverse axis is along the major axis of the conic,`x^2/3+y^2/4= 4` and has vertices atthe foci of this conic. If the eccentricity of the hyperbola is `3/2`, then which of the following points does NOT lie on it?A. `(sqrt(5),2sqrt(2))`B. `(sqrt(5),2sqrt(3))`C. `(0,2)`D. `(sqrt(10),2sqrt(3))`
Answer» The ellipse `(x^(2))/(3)+(y^(2))/(4)=4`, or `(x^(2))/(12)+(y^(2))/(16)=1` has its major axis along `y`-axis and eccentricity `e=sqrt(1-(12)/(16))=(1)/(2)`. So, coordinates of its foci are `(0,2)` and `(0,-2)` . The vertices of the hyperbola are at `(0,2)` and `(0,-2)` .So, the length of its transverse axis is `2b=4`. Let the length of its conjugate axis be `2a`. Then, `a^(2)=b^(2)(e^(2)-1)impliesa^(2)=4((9)/(4)-1)=5` So, the equation of the hyperbola is `(x^(2))/(5)-(y^(2))/(4)=-1` Clearly, `(5,2sqrt(3))` does not lie on this hyperbola.

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