20 algebra 2/geo
which is the equation of a parabola with a directrix at y = −3 and a focus at (−2, 3).

y = one twelfth(x − 2)squared
y = one twelfth(x + 2)squared
y = −one twelfth(x + 2)squared
y = −one twelfth(x − 2)squared

B

Step-by-step explanation:

For any point (x, y) on the parabola the distance from the focus and directrix are equal, that is

Using the distance formula

= | y + 3 |

Square both sides

(x + 2)² + (y - 3)² = (y + 3)² ← expand the factors in y on both sides

(x + 2)² + y² - 6y + 9 = y² + 6y + 9 ← subtract y² + 6y + 9 from both sides

(x + 2)² - 12y = 0 ← ( subtract (x + 2)² from both sides

- 12y = - (x + 2)² ( divide both sides by - 12 )

y = (x + 2)² → B

look at the photo below for the details

:)

x = 25/2304

step-by-step explanation: