Write the equation of a hyperbola with vertices (0, -4) and (0, 4) and foci (0, -5) and (0, 5). Please explain how to determine if the hyperbola is vertical or horitzontal?

llltkl | Student

The foci of the hyperbola has changing y-coordinates, hence it possesses a vertical transverse axis.

By the midpoint formula, the center of the hyperbola occurs at the point (0, 0). Its foci are at (0, 0+c) and (0, 0-c). Hence c=(5-0)=5 and a=(4-0)=4

Therefore, `b=sqrt(a^2-c^2)=sqrt(5^2-4^2)=3`

The standard form of its equation is:


`rArr y^2/16-x^2/9=1`