A parabola is a set of all points that?

Answer 1

• are the same distance from a point (known as its focus) and a line (known as its directrix)
• are given by y=x2, where x is real

There are other characterisations.

Apex Answer: are the same distance from a point and a line.

Answer 2

All points (x, y) which satisfy the equation y = ax^2 + bx + c for a given set of constants a, b and c where a is not zero.