Question 615752
To find the equation for a hyperbola. {{{(x-h)^2/a^2 - (y-k)^2/b^2 = 1}}} or {{{(y-k)^2/a^2 - (x-h)^2/b^2 = 1}}}, you need to be able to find the center, (h,k), the "a" and the "b" and you must be able to figure out if the hyperbola is vertically-oriented or horizontally-oriented.<br>
As you posted it, the problem does not contain enough information. The best you can do is<ul><li>Determine that the hyperbola is horizontally-oriented since the vertices are "side-by-side" instead of above and below each other.</li><li>Determine the center because the center is always halfway between the vertices.</li><li>Determine the "a" since "a" is the distance from the center to a vertex.</li></ul>There is no way to find the "b". Usually, in problems like this, you are given either the foci or the asymptotes.<br>
With the foci you can find the "c" and with the "c" and the "a" you can find "b".<br>
With the asymptotes you can find their slopes. And from the "a" and the slopes of the asymptotes you can find "b".