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Higher Mathematics. Circle. Unit 2 Outcome 4. Centre O (0,0) and radius r. x 2 + y 2 = r 2. DiscoveringTime. Friday, 07 November 2014. y. P( x , y ). r. O. Q. x. The equation of a circle centred on the origin. - PowerPoint PPT Presentation
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Higher Mathematics Unit 2 Outcome 4
DiscoveringTime Thursday 20 April 2023
Centre O (0,0)(0,0) and radius rr
x2 + y2 = r2
Circle
Let’s add another point Q on the x-axis so OQ = x and PQ = y.
xO
r
y
Using Pythagoras’ theorem:
OQ2 + PQ2 = OP2
So x2 + y2 = r2
The equation of a circle of radius r centred on the origin is x2 + y2 = r2
The equation of a circle of radius r centred on the origin is x2 + y2 = r2
x
y
P(x, y)
Q
The equation of a circle centred on the origin
Suppose we have a circle with its centre on the origin O and radius r.
If P(x, y) is any point on the circle we can write OP = r.
Higher Mathematics Unit 2 Outcome 4
discoveringtime.com Thursday 20 April 2023
Circle
Centre O (0,0)(0,0) and radius rrx2 + y2 = r2
State the radius of each circle
x2 + y2 = 49
x2 + y2 = 16 x2 + y2 = 36
x2 + y2 = 1
x2 + y2 = 100 x2 + y2 = 144
x2 + y2 = 9
x2 + y2 = 81
x2 + y2 = 64
x2 + y2 = 4
7
4
6
2
10
8
9
3
1
12
Higher Mathematics Unit 2 Outcome 4
DiscoveringTime Thursday 20 April 2023
Circle
Centre O (0,0)(0,0) and radius rrx2 + y2 = r2
Write the equation of the circle with the centre (0,0) and passing through
62 + 82 = r2
36 + 64 = r2
100 = r2
x2 + y2 = 100
a) (6,8)
b) (3,5)
32 + 52 = r2
9 + 25 = r2
34 = r2
x2 + y2 = 34
c) (-2,1)
-22 + 12 = r2
4 + 1 = r2
5 = r2
x2 + y2 = 5
d) (0, -3)
02 + -32 = r2
0 + 9 = r2
9 = r2
x2 + y2 = 9
Higher Mathematics Unit 2 Outcome 4
DiscoveringTime Thursday 20 April 2023
Circle
Centre O (0,0)(0,0) and radius rrx2 + y2 = r2
Write the equation of the circle with a centre origin and radius
r = 4
x2 + y2 = 16
a) 4
b) 7
x2 + y2 = 49
c) 9
x2 + y2 = 81
d) 12
x2 + y2 = 144
r2 = 16
r = 7
r2 = 49
r = 9
r2 = 81
r = 12
r2 = 144
Higher Mathematics Unit 2 Outcome 4
DiscoveringTime Thursday 20 April 2023
Circle
Find the centre and radius of the circles below
x2 + y2 = 7
x2 + y2 = 64
x2 + y2 = 11
x2 + y2 = 25
centre (0,0)
radius = 7
centre (0,0)
radius = 8
centre (0,0)
centre (0,0)
radius = 11
radius = 5
Higher Mathematics Unit 2 Outcome 4
DiscoveringTime Thursday 20 April 2023
To build skills
Complete Page 168
Exercise 1
Higher Mathematics Unit 2 Outcome 4
DiscoveringTime Thursday 20 April 2023
f) Remember to get the equation in correct format. Divide by 3
Question 1 Question 2
e) (sqrt 3 )2 = 3Draw a diagramPart ii) radius is the hypotenuse, use Pythagoras
Question 5
Question 6
2 values when you do a square root !!!
Question 7
Using skills. Method same as before
Remember to state final answer
Question 10 Question 11
Problem solvingDraw diagUse pythagoras
Question 8
Take care with layout. Ratio problem first Given 1 sec radius 2cm so
2sec radius 4cm etc
Plenary question ……
Higher Mathematics Unit 2 Outcome 4
DiscoveringTime Thursday 20 April 2023
Circle
x
y
Answer Radius of first circle is 2cm diam 4cm
diam of third circle is 8cmdiam of second circle is 6cm
diam of fourth circle is 10cm with a radius 5 cm
x2 + y2 = 25
A square emblem has a circle at its centre with equation
x2 + y2 = 4 The pattern repeats to the edge of the emblem with circles on the same centre with a radius of 1cm more each time.
The emblem side is 10 cm what is the equation of the largest circle on the emblem?
Exam standard question
Higher Mathematics Unit 2 Outcome 4
DiscoveringTime Thursday 20 April 2023
Circle
