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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)