Question

What is the equation of the parabola?

Answer 1

D

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

`√((x+6)^2+(y-0)^2)` = | x - 6 |, that is

`√((x+6)^2+y^2)` = | 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 = -
`(1)/(24)` y² → D