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