Review question

# Can we show these two circles lie entirely outside each other? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R6390

## Suggestion

Prove that the points whose coordinates satisfy the equation $x^2+y^2+2gx+2fy+c=0$ lie on a circle. State the coordinates of the centre of the circle and the length of its radius.

Do we know a standard form for the equation of a circle?

Can we rewrite the above equation into this form?

To “prove” the points are on a circle, we need to do more than state a standard equation. Can we show that all the points are the same distance from the centre?

Prove that the circles $x^2+y^2-20x-16y+128=0$ and $4x^2+4y^2+16x-24y-29=0$ lie entirely outside each other, and find the length of the shortest distance from a point on one circle to a point on the other.

Drawing a diagram will probably help.

Can we use the results from the first part of the question?