The spider's movement is an illustration of a parabola.
- The equation of a parabola is:

- The focus of a parabola is: (40,-30)
- The axis of symmetry is:

- The directrix is:

<u>(a) The equation</u>
The spider passes through the origin.
So, we have:

The spider jumps to a maximum height of 10mm, midway 80mm.
So, the vertex is:

The equation of a parabola is:

So, we have:

Subtract 10 from both sides


Solve for a

Substitute
and
in 

<u>(b) The focus, directrix and the axis of symmetry</u>
The focus of a parabola is:

Where:

So, we have:



So, we have:


The axis of symmetry is:

So, we have:

The directrix is:



Read more about parabolas at:
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