How to write equation of hyperbola with vertices at (0,-6) and (0,6) and foci at (0,-9) and (0,9)?
Since the center is in the middle of the foci, you can get the midpoint of (0,-9) and (0,9), which is (0,0). Since you know the vertices, you already know the length of the major axis. In hyperbolas, a^2+b^2=c^2, you can plug it in to find b. Then the equation of a hyperbola is ((x^2)/(a^2))+((y^2)/(b^2))=1. Sorry I don’t know how to do the squared sign on my keyboard.
Okay. So, first you have to find the midpoint which is X=(0+0)/2, Y=(6-6)/2, aka (0,0). Next, you find the distance from the foci to the origin, which is 9. Nine = C. After that, find the distance from the verticies to the center/origin, which is 6. Six = A. Furthermore, you have to use the formula C squared = A squared + B squared, or 81=36 + B squared. B= Root 45. Thus, once you put it into the hyperbola formula, you get (Y squared divided by 36) - (X squared divided by 45) = 1.