Question

What is the equation of the parabola with focus (3, 0) and directrix x = –3?

Answer 1

x =
`(1)/(12)` y²

Explanation:

Any point (x, y ) on the parabola is equidistant from the focus and the directrix

Using the distance formula, then

`√((x-3)^2+(y-0)^2)` = | x + 3 |

Squaring both sides

(x - 3)² + y² = (x + 3)² ← expanding both sides

x² - 6x + 9 + y² = x² + 6x + 9 ← subtract x² + 6x + 9 from both sides

- 12x + y² = 0 ( subtract y² from both sides )

- 12x = - y² ( divide both sides by - 12 )

x =
`(1)/(12)` y²

Answer 2

y²-12x = 0

Explanation:

The formula for calculating the equation of a parabola is y² = 4ax

and x = a

To find the equation of the parabola with focus (3, 0) and directrix x = –3,

The point given (x,y) = (3,0) and x = -3

From the data given, it can be seen that a = -3 by simply comparing x = a with x = -3

Similarly, x = 3 from the given point.

Substituting the value of x = -3 in the formula for equation of a parabola gives;

y² = 4(-3)x

y²= -12x

y²-12x = 0