How to identify "a" and "b" of a hyperbola with a provided equation? hey guys, i'm doing this homework assignment where i've got to find a and b parts of a hyperbola and i understand how to do this when the equation starts positive, but not when it begins with a negative. here's a screenshot of the question.. will appreciate any : )(this is precalc btw)

It works the same way if it begins negative, the negative in front of the 'x' terms just means that the hyperbola opens vertically.

'b' refers to distance from center to vertices in the 'y' direction because 'b' is with y term.

The vertices are at (0, +-4), b = 4

To find 'a' use the slope of the asymptotes.
slope = b/a = 4/a
Estimate slope by using a point that is farthest away from orgin, (10,20.5)
The asymptote will be slightly below the point (10,20)
This gives a slope of 20/10 = 2.
4/a = 2  > a = 4/2 = 2

  a = 2, b = 4