Hello, Zdmey!

There is a typo is #1 . . . the numbers don't fit.

1) Find the equation of a hyperbola with foci (-4,2) and (2,2)

and slope of one asymptote is 3/5 . . Could this be 4/5 ?

The foci are horizontally oriented.

Hence, the hyperbola is "horizontal": .

The center is halfway between the foci: .

. . And: .

The slope of the asymptotes is: .

If this slope is , then we have: .

Then is a multiple of 5, is a multiple of 4: .

Sincce , we have: .

. . Hence: .

The equation is: .