# To find: The equation of the given hyperbola.The foci of the hyperbola is (0, pm 5) and eccentricity is e-1.5.

To find: The equation of the given hyperbola. The foci of the hyperbola is .

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Step 1 Write the general equation of the hyperbola. The center of the hyperbola is , the vertice are , and foci are . Write the expression for c. Write the expression for the eccentricity of the hyperbola. The foci of the conic section are, Step 2 Write the expression for the eccentricity of the hyperbola. $e=\frac{c}{a}$ Substitute 5 for c and 1.5 for e. $1.5=\frac{5}{a}$
$a=3.33$ Write the expression for c. Substitute 3.33 for a and 5 for c.

$13.91={b}^{2}$
$b=3.73$ Write the general equation of the hyperbola. Substitute 3.33 for a, 0 for h, 3.73 for b, and 0 for k.
Therefore, the equation of the given hyperbola is .