A hyperbola is centered at C = (3,7). The vertices are (9,7) and (-3,7). The slopes of the asymptotes are m = + or - 5/6.
Enter the equation of the hyperbola in the form:
(x-h)^2/a^2 - (y-k)^2/b^2 = 1 or (y-k)^2/a^2 - (x-h)^2/b^2 = 1
Notice that the center and vertices have the same y-coordinate. This means that they lie on the same horizontal line, and the hyperbola's branches lie side by side (not above and below) each other - i.e. we have a parabola of the first form (of your equations above).
Hence, the slope of the asympotes are given by: `pm b/a.`
This gives us `b=5` and `a=6.`
The center gives us h and k. In this case, `h = 3` and `k = 7`.` `
Hence, our hyperbola is given by the following equation:
`((x - 3)^2)/36 - ((y - 7)^2)/25 = 1`