Prove that the points whose coordinates satisfy the equation x2+y2+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 x2+y2−20x−16y+128=0 and 4x2+4y2+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?
