Write the equation of a hyperbola satisfying the given condition:

with asymptotes y=-x and y=x+2 and vertical tranverse axis length of 4.

vertical tranverse axis

so hyperbola opens up and down

length of 4

so 2b=4, b=2

intersection of y=-x and y=x+2 is (-1,1)

so centre is (-1,1)

The equation so far is:

(x+1)² / a² - (y-1)² /2² = -1

But what is the value of a? How do you find a?

Thanks.