The foci and the directrices of the hyperbola are labeled. Which equation represents the hyperbola? (x-3)^2/16 - y^2/9= 1 x^2/16 - (y-3)^2/9= 1 (y-3)^2/9 - x^2/16= 1 y^2/9 - (x-3)^2= 1

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