Applications 1.2
Applying algebraic skills to circles
The Equation of a Circle

The equation of a circle, centre
Time
HHM 207 12D
(1 – 10)
period
the origin and radius r
 I have used Pythagoras to develop the equation of a circle with centre
the origin and radius r using 𝑥 2 + 𝑦 2 = 𝑟 2

The equation of a circle centre (a,b)
HHM 210 12F
(1 – 10)
period
and radius r
 I can determine the centre and radius of a circle given its equation using
(𝑥 − 𝑎)2 + (𝑦 − 𝑏)2 = 𝑟 2
 I can determine the equation of a circle given its centre and radius using
(𝑥 − 𝑎)2 + (𝑦 − 𝑏)2 = 𝑟 2
 I can use (𝑥 − 𝑎)2 + (𝑦 − 𝑏)2 = 𝑟 2 in mixed problems
 I can determine if a point lies inside, outside or on the circle

The general equation of a circle
HHM 213 12H
(1 – 16)
2 periods
 I can determine the centre and radius of a circle given its equation
using 𝑥 2 + 𝑦 2 + 2𝑔𝑥 + 2𝑓𝑦 + 𝑐 = 0 (Qu 1, 2, 3, 6, 11)
 I can identify when an equation in the form x2 + y2 + 2fx + 2fy + c = 0
represents a circle and then determine its radius (Qu 4, 5)

Intersection of a line and a circle
HHM 217 12J
(1 – 5)
1 period
 I can determine the point of intersection of a line and a circle or two circles

Tangents to circles
HHM 218 12K
(1 – 7)
1 period
(1 – 6)
1 period
 I can determine the point of intersection of a tangent to a circle

Equations of tangents
HHM 220 12L
 I can determine the equation of a tangent to a circle
TOTAL 7 periods