Conic Parabolas in General Form

[chaze]

Homework Statement

y² - 8x + 4y + 12 = 0

I need to find the vertex, focus, axis of symmetry, directrix, direction and p.

Homework Equations

N/A

The Attempt at a Solution

No attempt as this is the first one I've encountered in general form. I'm not even looking for an answer, but if someone knows where to find a website or tutorial which helps in solving a conic parabola in this form then it would be very helpful.

 

[Mark44]

Homework Statement

y² - 8x + 4y + 12 = 0

I need to find the vertex, focus, axis of symmetry, directrix, direction and p.

Homework Equations

N/A

The Attempt at a Solution

No attempt as this is the first one I've encountered in general form. I'm not even looking for an answer, but if someone knows where to find a website or tutorial which helps in solving a conic parabola in this form then it would be very helpful.

There are a couple of basic forms.
(y - k)² = 4p(x - h)

(x - h)² = 4p(y - k)

The first form above opens to the left or right, depending on whether p is negative or positive.

The second form opens down or up, depending on whether p is negative or positive.

In both, the vertex of the parabola is at (h, k), the focus is inside the parabola, and |p| units from the vertex, located on the axis of symmetry. The directrix is on the outside of the parabola, and |p| units the other way from the vertex.

For your problem, put the y terms on one side and the x terms on the other, and complete the square in the y terms. It should look like the first form above.