Answer:
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
