Answer:
D
Step-by-step explanation:
From any point (x, y ) on the parabola the focus and directrix are equidistant
Here the focus = (- 6, 0) and the directrix is x = 6
Using the distance formula
[tex]\sqrt{(x+6)^2+(y-0)^2}[/tex] = | x - 6 |, that is
[tex]\sqrt{(x+6)^2+y^2}[/tex] = | x - 6 |
Squaring both sides
(x + 6)² + y² = (x - 6)² ← distribute factors on both sides
x² + 12x + 36 + y² = x² - 12x + 36
Subtract x² - 12x + 36 from both sides
24x + y² = 0 ( subtract y² from both sides )
24x = - y² ( divide both sides by 24 )
x = - [tex]\frac{1}{24}[/tex] y² → D
