Answer:
Step-by-step explanation:
Hyperbola are generally written as
(x-h)² / a² - (y-k)² / b² = 1
Where,
(h, k) is the center is
"a" is the semi-transverse axis
"b" is the semi-conjugate axis
The focus and the directives is generally describe as
The foci of the graph are
(h + a⋅e, k) and (h − a⋅e, k)
The directrices of the graph are
x = h + a / e and x = h − a / e
Comparing this to the equation given
1. (x-3)² / 4² - y² / 3² = 1
This is an hyperbole of centre (3,0)
And parallel to the x axis
2. x² / 4² - (y-3)² / 3² = 1
This is also an hyperbole of center (0,3) and parallel to the x axis
3. (y-3)² / 3² - x² / 4² = 1
This is an hyperbole parallel to the x axis
4. y² / 3² - (x-3)² / 1² = 1
This is an hyperbole parallel to the y-axis
