# Teacher Notes

### Why use this resource?

There’s a beautiful result about parabolas in this resource.

Once students have started thinking about the problem, they will find it more accessible than it looks, and it’s a useful opportunity to recognise the difference of two squares in a less routine context.

### Possible approach

It is worth discussing the first result and the use of difference of two squares before moving on to the problem about midpoints.

Note that the position of $A$ in the diagram means that $a$ is negative, so it may be worth asking students to consider whether their argument holds for any points $A$ and $B$ on the parabola.

### Key questions

• What is the gradient of the chords $AB$ and $OC$?

• How do you find the coordinates of the midpoint of $A$ and $B$?