## 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.