Question

When using the equation y^2 = 4ax to find the equation of a parabola, how do I know what "a" is?

Answer 1

Example,
Question: Find an equation of the parabola with vertex at (0, 0) and focus at (3, 0).

Solution: The distance form the vertex (0, 0) to the focus (3, 0) is a = 3. Based on equation 2, the equation of this parabola is

\(y^2 = 4ax\)
\(y^2 = 12x\)

Answer 2

Where do they get the 3 from?

Answer 3

They get the 3 from the focus.

http://prntscr.com/9ds9no

Answer 4

This was a huge struggle point last year for me >_<

Answer 5

So the x coordinate of the focus is "a"?

Answer 6

Yup :)

Answer 7

So,
Question: Find an equation of the parabola with vertex at (1, 2) and focus at (4, 8).

Would "a" still be 4?

Answer 8

And depending on the equation, the graph will look differently. And from the equation you can tell where the focus would be by knowing what 'a' is :)

Answer 9

Idek if that would be a possible vertex and focus, just an example

Answer 10

For that kind of question, you have to use another formula:

(x-h)^2 = 4p(y-k)

Answer 11

How do I know what h, k and p are?

Answer 12

Vertex is (h, k) right?

Answer 13

As always, (h,k) is the vertex

Answer 14

And, for p

"The absolute value of p is the distance between the vertex and the focus and the distance between the vertex and the directrix."

Answer 15

My book says 4a, is there any difference between p and a?

Answer 16

I guess not lol

Answer 17

http://www.purplemath.com/modules/parabola3.htm :)