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.