Circles

IntroductionCircle equation

Circle propertiesPractice qs

Points of intersection

IntroductionA circle is the set of all points a fixed distance from a fixed point

In general the equation of a circle centre (0,0) and radius r is

x 2 + y 2 = r2

What is the equation of a circle centre (0,0) of radius 4?

General equation of a circleNow move the circle so it has centre (a,b) and radius r

The equation of a circle centre (a,b) and radius r is: (x - a)2 + (y - b)2 = r2

(a,b)

You need to know this!

Examples

Write down the equation of a circle with centre (-5, 9) and radius 6.

Find the equation of the circle through (6,9) with centre (4,3)

Find the centre and radius of the circle

(x - 4)2 + (y + 2)2 = 49

Now do Ex 13A page 199 qs 1, 2(a) (b) (c) 4, 5

Circle properties

The angle in a semicircle is a right angle.

The perpendicular from the centre to a chord bisects the chord.

The tangent to a circleis perpendicular to theradius at its point of contact.

Finding points of intersection

You may be asked to find the points of intersection between a circle and a line.

Remember 3 things that could happen

For intersections always think Simultaneous Equations!

Finding points of intersection

Find the points of intersection of the circle x2 + y2 = 25 and the line x + y = 7