Find \( a \) and \( b \) for the ellipse \( b^{2} x^{2}+a^{2} y^{2}=a^{2} b^{2} \) if the distan...

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Find \( a \) and \( b \) for the ellipse \( b^{2} x^{2}+a^{2} y^{2}=a^{2} b^{2} \) if the distance between the directrices is \( 5 \sqrt{5} \) and the distance between the foci is \( 4 \sqrt{5} \).
(a) \( a= \pm 5, b= \pm \sqrt{5} \)
(b) \( a= \pm \sqrt{5}, b= \pm 5 \)
(c) \( a= \pm 5 \sqrt{5}, b= \pm 5 \sqrt{5} \)
(d) None of these
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