If the foci of `(x^2)/(a^2)-(y^2)/(b^2)=1` coincide with the foci of `(x^2)/(25)+(y^2)/9=1` and the eccentricity of the hyperbola is 2, then

Options

A. `a^(2)+b^(2)=16`
B. there is no director circle to the hyperbola
C. the centre of the director circle is (0, 0)
D. the length of latus rectum of the hyperbola is 12

Answer

A, B, D

Explanation

For the ellipse,
`a=5 and e=sqrt((25-9)/(25))=(4)/(5)`
`therefore" "ae=4`
Hence, the foci are `(-4, 0) and (4,0)`.
For the hyperbola
`ae=4, e=2`
`therefore" "a=2`
`b^(2)=4(4-1)=12`
`"or "b=sqrt(12)`