Parametric equations: eliminating the parameter

Two introductory examples of eliminating the parameter in parametric equations

[ChipperMoMo]

You are the best person in the world for uploading these videos. Never stop man. Never frikken stop!

[davidmetzler]

The 4 distributes over the (x+1/2)^2 (where it *doesn't* cancel) and the -1/4 (where it does). So it remains in front of the (x+1/2)^2.

[sophielamoureux]

5:09 thought the 4 cancelled out with the -1/4 and left the -1 to cancel out with the +1... So why is the 4 still there?