Visualising maths

Parabolas - effect of parameter ‘a’

This section looks at the effect of changing the parameter $a$ in the Cartesian equation of the parabola $y^2 = 4 a x$.

Changing the value of $a$ moves the position of the focus and the directrix, which in turn changes the curve. The smaller the value of $a$, the closer the focus and directrix are to the origin.

Use the buttons to set the value of $a$ to different values, and see the effect on the curve.

Making $a$ smaller makes the parabola itself smaller. Viewed on the same axes, this makes the parabola appear narrower and more “pointed” - but in fact that is simply because you are seeing more of the parabola. In fact, all parabolas are the same shape.