THE CIRCLE

CIRCLE EQUATIONS.

1.                                     Centre (0,0)                 radius r.

2.                     Centre (h, k)                radius r.

3.              Centre           radius

INTERSECTION OF A LINE AND A CIRCLE.

Use simultaneous equations.

TANGENTS.

A tangent is perpendicular to a radius at the point of contact. Use .

The equation of a tangent to the circle  at the point

is given by

A tangent intersects a circle at one point only. The equation  may be useful.

CHORDS

A chord intersects the circle at two points.

A radius meets the centre of a chord at right angles. Use .

PARAMETRIC EQUATION OF A CIRCLE.

This does not have to be learned.

Given x as a function and y as a function change it into formula 1 or 2 above.
If the functions are trigonometric, get sine (or cos) on its own and square.
Use the golden rule:

TOUCHING CIRCLES.

The distance between two touching circles equals either the sum or the difference of the radii.