Question 982288
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Close, but no cigar.  For a hyperbola centered at the origin, the vertices are at (0,-a) and (0,a).  You were correct to say that a and b are in the ratio 5/4 because of the slopes of the asymptote equations, but you left off the step where you should have calculated the correct value of b based on the fact that a = 10 because of the specification of the vertices.


*[tex \LARGE \ \ \ \ \ \ \ \ \ \  \frac{5}{4}\ =\ \frac{b}{10}]


Solve for b and give your equation another try.


John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
My calculator said it, I believe it, that settles it

*[tex \Large \ \
*[tex \LARGE \ \ \ \ \ \ \ \ \ \