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.
$a$ 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.