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