# Homework Help: Parabola Problem

1. Aug 1, 2007

### bengaltiger14

1. The problem statement, all variables and given/known data

Find the focus of parabola: y:-(1/4)x^2 + 2x - 5

3. The attempt at a solution

Multiplying by 4 to get rid of fraction I get:
4y:-x^2 + 2x - 5

I will bring over the -5:
4y+5:-x^2 +2x

Completing Square I obtain:

4y+6:-(x-1)^2

Is all this correct thus far?

2. Aug 1, 2007

### Irid

Do you know what a focus of a parabola is? I think it has something to do with polar coordinates.

3. Aug 1, 2007

### bengaltiger14

The focus is the central point of a parabola I believe. It determines if parabola points up or down

4. Aug 1, 2007

### Irid

That is the extreme point of a parabola, not a focus.

A physical definition for focus could be this: If you shine parallel beams of light on the parabolic surface, it all reflects and focuses in a special point, called a focus. (A parabolic telescope).

A mathematical one: every point of a parabola has equal distances to a line and a point. The point is called a focus.

Further, if you write down the equation of parabola in polar coordinates in its simplest form, the pole is the focus of parabola.

5. Aug 1, 2007

### Dick

All very true. But you don't NEED polar coordinates. If you write a standard form for the parabola in cartesian coordinates x^2=4ay the vertex is at the origin and the distance from vertex to focus is 'a'. You just have to write your quadratic in a form similar to the standard form. Like (x-x0)^2=4a(y-y0). Now you have vertex at (x0,y0) and distance to focus 'a'.