1. ## Coordinate systems

Find, in cartesian form, an equation of the parabola whose focus and directrix are respectively (3, 0), x+5 = 0.

How can I find?

As I know y^2 = 4ax is a cartesian equation of the parabola. And every point on the parabola is equidistant from the focus (a, 0) and the directrix x+a = 0.

But here, there are 2 different values of a.

2. Originally Posted by geton
Find, in cartesian form, an equation of the parabola whose focus and directrix are respectively (3, 0), x+5 = 0.

How can I find?

As I know y^2 = 4ax is a cartesian equation of the parabola. And every point on the parabola is equidistant from the focus (a, 0) and the directrix x+a = 0.

But here, there are 2 different values of a.
$\displaystyle y^2 = 4ax$ represents a parabola that opens either to the right or left. Yours opens to the right, so a is positive. The perpendicular line between the focus and the directrix is bisected by the vertex, so your vertex is at (-1, 0). Does this help?

-Dan

3. Originally Posted by topsquark
$\displaystyle y^2 = 4ax$ represents a parabola that opens either to the right or left. Yours opens to the right, so a is positive. The perpendicular line between the focus and the directrix is bisected by the vertex, so your vertex is at (-1, 0). Does this help?

-Dan
Yes I got it. a's value is 4 actually. And by substitution, I got y^2 = 16x + 16.

Thank you.