To find the hyperbolic equation with the same focus as the ellipse X & # 178 / 16 + Y & # 178 / 8 = 1, the asymptotic equation is x ± √ 3Y = 0

If the asymptotic equation is x ± √ 3Y = 0, then let the hyperbolic equation be x ^ 2-3y ^ 2 = k, (k > 0)
That is, x ^ 2 / K-Y ^ 2 / (K / 3) = 1
The focus coordinates are C ^ 2 = 16-8 = 8
That is, K + K / 3 = 8
k=6
That is, the hyperbolic equation is x ^ 2 / 6-y ^ 2 / 2 = 1

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