Simple parabola solving problem

[thunderhadron]

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 -



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



Solving these equations I'll get -



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



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.

 

[voko]

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

 

[HallsofIvy]

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.