Write the equation of a parabola with a vertex and (-5, 2) and a directrix y = - 1

y = (x+5) ²/6 + 1/3

Step-by-step explanation:

Use the distance formula to plug in the values you know:

√ (y+1) ² = √ (x+5) ² + (y-2) ²

the square roots cancel out

(y+1) ² = (x+5) ² + (y-2) ²

(y+1) (y-1) = (x+5) ² + (y-2) (y-2)

y²+2y+1 = (x+5) ² + y² - 4y+4

the y² cancel out

2y + 4y = (x+5) ² + 4-1

6y = (x+5) ² + 3

y = (x+5) ² / 6 + 1/3