### Circles

Package of problems

# Elliptical crossings Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

## Problem

This diagram shows the ellipse with equation $x^2+4y^2=16$ together with the straight line $y=x+c$.

The line and ellipse intersect at the points $A$ and $B$, and the midpoint of $AB$ is $M$.

Find the coordinates of $M$ for some different values of $c$.

What do you notice?

What would happen if you used straight lines of a different gradient instead?