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AS Core Maths-TAM Online Session 2: Coordinate Geometry A warm question to look at while you are waiting
If A is (1,0) and B is (0,-3), what are the equations of the lines making up the rectangle?
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Session Content
Straight lines
Circles
This is content based on chapter 2 in the AS Core textbook
The Basics
Coordinates of A & B
Distance AB Midpoint of
AB Gradient of
AB
(-4,-8) (-2,-4) (0,5) (6,1) (-1,3) (-7,9) (1, 7) (3,9 ) (-3,8) (6,5)
(-4,-6)
-1
What is meant by ‘the equation of a line’?
Parallel and perpendicular lines
Back to that starter question…
A(1,0)
B(0,-3)
Circles and Pythagoras
The general circle
Sketch the circle
COPY A
Sketch the circle
COPY B
Sketch the circle
COPY C
Sketch the circle
COPY D
Sketch the circle
COPY E
Sketch the circle
COPY F
Concentric circles( x −3 )2+ ( y− 4 )2=16
Concentric circles (2)
𝑥2−6 𝑥+ 𝑦2− 8 𝑦=0a)
c)b)
d)
Which one is the equation of a circle?
A:
B:
C:
D:
Which one is the equation of a circle?
A:
B:
C:
D:
A few questions to promote thinking…
The circle has centre (2, 3) and radius 5. What are the lengths of tangents to (10,0)?
10
−2
2
4
6
8
x
y
A
B
A few questions to promote thinking…
Find the equation of the circle passing through any 3 points of your choice
A few questions to promote thinking…
Find the equation of the small circle
A few questions to promote thinking…
Find the equations of the line and the circle
A few questions to promote thinking…
Session content check• Straight lines• Circles
MEI C1 JUNE 2010 NO. 3
AQA C1 May 2012 no. 2
MEI C1 JUNE 2010 NO. 10
EDEXCEL C2 Jan 2013 no. 55. The circle C has equation
x2 + y2 − 20x − 24y + 195 = 0. The centre of C is at the point M. (a) Find (i) the coordinates of the point M, (ii) the radius of the circle C.
(5) N is the point with coordinates (25, 32). (b) Find the length of the line MN.
(2) The tangent to C at a point P on the circle passes through point N. (c) Find the length of the line NP.
(2)
OCR C1 May 2012 NO. 10
EDEXCEL C2 JUNE 2013 NO. 10
Figure 4 The circle C has radius 5 and touches the y-axis at the point (0, 9), as shown in Figure 4. (a) Write down an equation for the circle C, that is shown in Figure 4.
(3)
A line through the point P(8, –7) is a tangent to the circle C at the point T. (b) Find the length of PT.
(3)