# Equation of the parabola help

1. Oct 3, 2007

### srujana_09

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

2. Relevant equations

3. The attempt at a solution

Last edited by a moderator: May 12, 2014
2. Oct 3, 2007

### srujana_09

Can we find the equation of the parabola when only two points on it are known and neither of them is the focus nor the vertex?

3. Oct 3, 2007

### symbolipoint

No. Three points are needed. If you mean to find a specific equation, the general form for a parabola equation has three constants which must be treated as variables; the coordinate values become the known values. You will need 3 equations, and have 3 unknowns - you are looking for the three unknown constants.

You need any three points on the curve, $$$(x_1 ,y_1 ),\;(x_2 ,y_2 ),\;(x_3 ,y_3 )$$$
$$$\begin{array}{l} y_1 = ax_1^2 + bx_1 + c \\ y_2 = ax_2^2 + bx_2 + c \\ y_3 = ax_3^2 + bx_3 + c \\ \end{array}$$$

4. Oct 3, 2007

### Feldoh

Well technically you could make infinitely many parabola's with two different points couldn't you?

5. Oct 3, 2007

### HallsofIvy

Staff Emeritus
I'm concerned about the way that is phrased. Do you understand that the focus of a parabola is never on the parabola?