Question

Can someone please help me with the following?

Answer 1

y^2 = -12x

Step-by-step explanation:

For a parabola whose vertex is at (0,0), its standard equation is

`y^2=-4ax`

where the directrix is given by x = a.

Now in our case, the vertex of our parabola is at (0,0) and the directrix is x = 3. This tells us that a = 3 and so the above equation gives

`y^2=-4\cdot3x`

`\boxed{y^2=-12x\text{.}}`

which is our answer!