Review question

# Can we find the circles through the points where two ellipses meet? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R8216

## Suggestion

Show that the equation of any circle passing through the points of intersection of the ellipse $(x + 2)^2 + 2y^2 = 18$ and the ellipse $9(x - 1)^2 + 16y^2 = 25$ can be written in the form $x^2 - 2ax + y^2 = 5 - 4a.$

Can we sketch the ellipses roughly? In how many points will the two ellipses meet? How can we find these points?

Where will the centres of circles going through the intersection points lie?