Question 1136851
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Clearly there are two asymptotes; if the equation of one of them is y=(3/5)x, then the equation of the other is y = (-3/5)x.<br>
The coordinates of the vertices, and also the fact that the asymptotes pass through the origin, tell us that the center of the hyperbola is at the origin.<br>
And the vertices on the y-axis tell us that the branches of the hyperbola open up and down.<br>
The standard form of the equation of a hyperbola with center at the origin and branches opening up and down is<br>
{{{y^2/a^2-x^2/b^2 = 1}}}<br>
a is the distance from the center to each vertex, so you know a; all you need to finish the equation is b.<br>
For that, use the fact that the slopes of the asymptotes are a/b and -a/b.