# Simple parabola solving problem

1. Jul 6, 2013

Hi friends I am sticking in solving a parabola equation. Please help me in solving this issue.

The problem is as follows -

I have given three points which are as follows -

[Broken]

These points are lying on a parabola whose equation is Y2 = 4AX

If these points are lying on this parabola hence will satisfy its equation.

Hence

Placing all the points in the equation Y2 = 4AX

[Broken]

Solving these equations I'll get -

[Broken]

But friends the problem is that, when I am solving these equations in different manner - - -

[Broken]

I am getting the wrong answer. The previous answer was right i.e. a√7 / 2.

Why this is happening. Please friends help me in finding this issue.

Thank you all very much in advance.

Last edited by a moderator: May 6, 2017
2. Jul 6, 2013

### voko

The point $(x_1, y_1) = (0, a/2)$ is not compatible with the equation $y^2 = 4Ax$.

3. Jul 6, 2013

### HallsofIvy

Staff Emeritus
$y^2= 4Ax$ is a parabola through the origin and symmetric about x= 0. The more general form would be $x= ay^2+ bx+ c$ or $x= a(y- y_0)^2+ x_0$.

Notice that while your form has only the single parameter, A, those have three parameters which can be determined by three equations.