Question

The parabola whose equation is y 2 = 12x has directrix of:

x = 3
x = -3
y = 3
y = -3

Answer 1

x=-3

Explanation:

The general equation of a parabola with vertex at the origin is

`y^2=4ax`

in the case that it opens horizontally and

`x^2=4ay`

in the case that it opens vertically. Moreover, in the case that the parabola opens horizontally, the point (0,a) is the focus of the parabola, and the directriz is the vertical line x=-a. The same is true but with interchanged coordinates for a parabola that open vertically.

In our case

`y^2=12x=4\cdot3x`

is a parabola that opens to the right with focus point (0,3) and vertical directriz

x=-3.

Answer 2

The parabola whose equation is y 2 = 12x has directrix of:
x = 3
x = -3
y = 3
y = -3

The directrix is:
x=-3

One way of solving is to assign values for x and y:
x y
0 0
1 3.46
1 -3.46
2 4.9
2 -4.9


When graphed, the solution is:
Direction: Opens RightVertex: (0,0)(0,0)Focus: (3,0)(3,0)Axis of Symmetry: y=0Directrix: x=−3