Download UNIT 2 – ANALYTIC GEOMETRY (Lesson 7 – Equation of a Circle)

UNIT 2 – ANALYTIC GEOMETRY
(Lesson 7 – Equation of a Circle)
2 2  4
Note:
=
5  5  25
In General,
 x  x
2
=
The Circle
Development of the Circle – set of points P(x, y) having centre O(0,0) and radius r.
→ Determine the length of OP using the length formula.
∴ The equation of a circle with centre O(0, 0) and radius r is ___________________.
Example 1: Write an equation for the circle with centre (0,0) and the given radius
a) r = 5
b) r = 9
Example 2:
a)
Determine the radius of each circle, to the nearest tenth where necessary.
x  y2  9
2
b)
x 2  y 2  26
Example 3:
Determine the radius of each circle, given its centre and a point on its
circumference. Round where necessary.
a) centre (0,0), pt. (5, 12)
b) centre (0,0), pt. (-2, 3)
Example 4: Is the point (-5, 9) inside the circle x 2  y 2  100
2
2
Example 5: Is the point (12, 5) on the circle x  y  169