This is what I have so far, but I’m not sure what I need to fix. please help asap!!

I think your answer is correct already. You just have to put your latus rectum, directrix, and focus into your drawing. :)

for asymptotes:

Let's change the centers into (-3, 2). Therefore, (y-2)² - (x+3)²/16 = 1

To get the asymptotes, let's equate the equation to zero (0) instead of one (1).

(y-2)² - (x+3)²/16 = 0

Notice that this equation is the difference of two squares.

Let x² = (y-2)² and y² = (x+3)²/16

Therefore, we have x² - y² =0

The factors of two squares are:

(x+y)(x-y)=0

Then, equating each factor to zero:

x+y=0

x-y=0

Substituting the real equations:

» (y-2) + (x+3)/4 = 0

y-2 = - (x+3)/4

y= -(x+3)/4 + 2

» (y-2) - (x+3)/4 = 0

y-2 = (x+3)/4

y= (x+3)/4 +2