# How Can I Get This Equation From These 3 Equations

Hi, I've Read an Article That Says:
If:
EQ.1:

and EQ2:
http://latex.codecogs.com/gif.latex?x=vtcos(\theta)

and EQ3:
http://latex.codecogs.com/gif.latex?y=-\frac{1}{2}gt^2 &plus; vtsin(\theta)

We Can Get The Following Equation (an Ellipse Equation) By Substituting t(EQ1) into EQ.2 and EQ.3 Using StraightForward Algebra:
http://latex.codecogs.com/gif.latex?(y-\frac{v^2}{4g})^2 &plus; \frac{1}{4}x^2=(\frac{v^2}{4g})^2

But How it is Possible?!

Last edited:

$$y= - \frac{g}{2v^2 \cos^2\theta} \left( x - \frac{ v^2 \sin(2\theta)}{2 g } \right)^2 + \frac{ v^2 \sin^2\theta}{2 g }.$$