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: .