Question

Find an equation of a parabola with a vertex at the origin of directrix Y = -2.5

Answer 1

Answer:

$y=\frac{1}{10}x^2$

Step-by-step explanation:

Since the directrix is $y=-2.5$, it means the axis of the parabola is parallel to the y-axis.

Also, the vertex is at the origin so the parabola opens upwards.

The equation of a parabola with these properties is of the form $x^2=4py$, where $|p|=2.5$,that is the distance between the vertex and the directrix.

$\Rightarrow p=-2.5\:or\:2.5$.

Since the parabola opens upwards, we choose $p=2.5$.

The equation of the parabola now becomes,

$x^2=4(2.5)y$

$\Rightarrow x^2=10y$

Or

$y=\frac{1}{10}x^2$

See graph