Finding the Equation of a Parabola with Two Known Points

[srujana_09]

 

[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?

 

[symbolipoint]

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?

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, $$\[<br /> (x_1 ,y_1 ),\;(x_2 ,y_2 ),\;(x_3 ,y_3 )<br /> \]$$
$$\[<br /> \begin{array}{l}<br /> y_1 = ax_1^2 + bx_1 + c \\ <br /> y_2 = ax_2^2 + bx_2 + c \\ <br /> y_3 = ax_3^2 + bx_3 + c \\ <br /> \end{array}<br /> \]$$

 

[Feldoh]

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?

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

 

[HallsofIvy]

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?

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