Circles Introduction Circle equation Circle properties Practice qs Points of intersection.

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Presentation transcript:

Circles Introduction Circle equation Circle properties Practice qs Points of intersection

Introduction A 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 = r 2 What is the equation of a circle centre (0,0) of radius 4?

General equation of a circle Now 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 = r 2 (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 circle is perpendicular to the radius 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 x 2 + y 2 = 25 and the line x + y = 7