Standard Parabolas
Parabolas can open rightward, open leftward, open upward and open downward.
Open Leftward
y2 = −4ax [a> 0]
If x > 0, then y becomes imaginary. i.e., the curve does not exist for x > 0 i.e., the curve exist for x ≤ 0.
Open Upward
x2 = 4ay [a> 0]
If y < 0, then y becomes imaginary. i.e., the curve does not exist for y < 0 i.e., the curve exist for y ≥ 0.
Open Downward
x2 = −4ay [a > 0]
If y > 0, then y becomes imaginary. i.e., the curve does not exist for y > 0 i.e., the curve exist for y ≤ 0.