- The ellipse \(E\) has equation
$$\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 9 } = 1$$
The hyperbola \(H\) has equation
$$\frac { x ^ { 2 } } { a ^ { 2 } } - \frac { y ^ { 2 } } { b ^ { 2 } } = 1$$
where \(a\) and \(b\) are positive constants.
Given that
- the eccentricity of \(H\) is the reciprocal of the eccentricity of \(E\)
- the coordinates of the foci of \(H\) are the same as the coordinates of the foci of \(E\) determine
- the value of \(a\)
- the value of \(b\)