analytical geometry past papers (questions &...

Compiled by Navan Mudali

NicZenDezigns Page 1 of 134

Analytical Geometry – Past Papers (Questions & Solutions)

November 2008

Compiled by Navan Mudali

NicZenDezigns Page 2 of 134

Compiled by Navan Mudali

NicZenDezigns Page 3 of 134

Compiled by Navan Mudali

NicZenDezigns Page 4 of 134

Compiled by Navan Mudali

NicZenDezigns Page 5 of 134

Compiled by Navan Mudali

NicZenDezigns Page 6 of 134

Compiled by Navan Mudali

NicZenDezigns Page 7 of 134

Compiled by Navan Mudali

NicZenDezigns Page 8 of 134

Compiled by Navan Mudali

NicZenDezigns Page 9 of 134

Compiled by Navan Mudali

NicZenDezigns Page 10 of 134

Compiled by Navan Mudali

NicZenDezigns Page 11 of 134

November 2009

Compiled by Navan Mudali

NicZenDezigns Page 12 of 134

Compiled by Navan Mudali

NicZenDezigns Page 13 of 134

Compiled by Navan Mudali

NicZenDezigns Page 14 of 134

Compiled by Navan Mudali

NicZenDezigns Page 15 of 134

Compiled by Navan Mudali

NicZenDezigns Page 16 of 134

Compiled by Navan Mudali

NicZenDezigns Page 17 of 134

Compiled by Navan Mudali

NicZenDezigns Page 18 of 134

Compiled by Navan Mudali

NicZenDezigns Page 19 of 134

Compiled by Navan Mudali

NicZenDezigns Page 20 of 134

February 2010

Compiled by Navan Mudali

NicZenDezigns Page 21 of 134

Compiled by Navan Mudali

NicZenDezigns Page 22 of 134

Compiled by Navan Mudali

NicZenDezigns Page 23 of 134

Compiled by Navan Mudali

NicZenDezigns Page 24 of 134

Compiled by Navan Mudali

NicZenDezigns Page 25 of 134

Compiled by Navan Mudali

NicZenDezigns Page 26 of 134

November 2010

Compiled by Navan Mudali

NicZenDezigns Page 27 of 134

Compiled by Navan Mudali

NicZenDezigns Page 28 of 134

Compiled by Navan Mudali

NicZenDezigns Page 29 of 134

Compiled by Navan Mudali

NicZenDezigns Page 30 of 134

Compiled by Navan Mudali

NicZenDezigns Page 31 of 134

Compiled by Navan Mudali

NicZenDezigns Page 32 of 134

Compiled by Navan Mudali

NicZenDezigns Page 33 of 134

Compiled by Navan Mudali

NicZenDezigns Page 34 of 134

Compiled by Navan Mudali

NicZenDezigns Page 35 of 134

Compiled by Navan Mudali

NicZenDezigns Page 36 of 134

Compiled by Navan Mudali

NicZenDezigns Page 37 of 134

February 2011

QUESTION 4

In the diagram below PQR with vertices P(– 1 ; 2), Q(– 2 ; – 2) and R(3 ; 0) is given.

-5 -4 -3 -2 -1 1 2 3 4 5

-5

-4

-3

-2

-1

1

2

3

4

5

x

Q

P

RO

y

4.1 Calculate the angle that PQ makes with the positive x-axis. (3)

4.2 Determine the coordinates of M, the midpoint of PR. (2)

4.3 Determine the perimeter of PQR to the nearest whole number. (5)

4.4 Determine an equation of the line parallel to PQ that passes through M. (3)

[13]

Compiled by Navan Mudali

NicZenDezigns Page 38 of 134

QUESTION 5

5.1 The equation of a circle is 156822 yxyx .

5.1.1 Prove that the point (2 ; – 9) is on the circumference of the circle. (2)

5.1.2 Determine an equation of the tangent to the circle at the point (2 ; – 9). (7)

5.2 Calculate the length of the tangent AB drawn from the point A(6 ; 4) to the circle with equation

10)1()3( 22 yx .

(5)

[14]

QUESTION 6

The circle, with centre A and equation 25)2()3( 22 yx is given in the following diagram. B is a

y-intercept of the circle.

x

y

O

6.1 Determine the coordinates of B. (4)

6.2 Write down the coordinates of C, if C is the reflect ion of B in the line x = 3. (2)

6.3 The circle is enlarged through the origin by a factor of 2

3.

Write down the equation of the new circle, centre A/, in the form

222 )()( rbyax .

(2)

B C

A

Compiled by Navan Mudali

NicZenDezigns Page 39 of 134

6.4 In addition to the circle with centre A and equation 25)2()3( 22 yx , you are given the

circle 100)10()12( 22 yx with centre B.

6.4.1 Calculate the distance between the centres A and B. (2)

6.4.2 In how many points do these two circles intersect? Justify your answer. (2)

[12]

Compiled by Navan Mudali

NicZenDezigns Page 40 of 134

Compiled by Navan Mudali

NicZenDezigns Page 41 of 134

Compiled by Navan Mudali

NicZenDezigns Page 42 of 134

Compiled by Navan Mudali

NicZenDezigns Page 43 of 134

Compiled by Navan Mudali

NicZenDezigns Page 44 of 134

November 2011

Compiled by Navan Mudali

NicZenDezigns Page 45 of 134

Compiled by Navan Mudali

NicZenDezigns Page 46 of 134

Compiled by Navan Mudali

NicZenDezigns Page 47 of 134

Compiled by Navan Mudali

NicZenDezigns Page 48 of 134

Compiled by Navan Mudali

NicZenDezigns Page 49 of 134

Compiled by Navan Mudali

NicZenDezigns Page 50 of 134

Compiled by Navan Mudali

NicZenDezigns Page 51 of 134

Compiled by Navan Mudali

NicZenDezigns Page 52 of 134

Compiled by Navan Mudali

NicZenDezigns Page 53 of 134

Compiled by Navan Mudali

NicZenDezigns Page 54 of 134

Compiled by Navan Mudali

NicZenDezigns Page 55 of 134

February 2012

Compiled by Navan Mudali

NicZenDezigns Page 56 of 134

Compiled by Navan Mudali

NicZenDezigns Page 57 of 134

Compiled by Navan Mudali

NicZenDezigns Page 58 of 134

Compiled by Navan Mudali

NicZenDezigns Page 59 of 134

Compiled by Navan Mudali

NicZenDezigns Page 60 of 134

Compiled by Navan Mudali

NicZenDezigns Page 61 of 134

Compiled by Navan Mudali

NicZenDezigns Page 62 of 134

Compiled by Navan Mudali

NicZenDezigns Page 63 of 134

November 2012

Compiled by Navan Mudali

NicZenDezigns Page 64 of 134

Compiled by Navan Mudali

NicZenDezigns Page 65 of 134

Compiled by Navan Mudali

NicZenDezigns Page 66 of 134

Compiled by Navan Mudali

NicZenDezigns Page 67 of 134

Compiled by Navan Mudali

NicZenDezigns Page 68 of 134

Compiled by Navan Mudali

NicZenDezigns Page 69 of 134

Compiled by Navan Mudali

NicZenDezigns Page 70 of 134

Compiled by Navan Mudali

NicZenDezigns Page 71 of 134

Compiled by Navan Mudali

NicZenDezigns Page 72 of 134

Compiled by Navan Mudali

NicZenDezigns Page 73 of 134

Compiled by Navan Mudali

NicZenDezigns Page 74 of 134

Compiled by Navan Mudali

NicZenDezigns Page 75 of 134

Compiled by Navan Mudali

NicZenDezigns Page 76 of 134

Compiled by Navan Mudali

NicZenDezigns Page 77 of 134

February 2013

Compiled by Navan Mudali

NicZenDezigns Page 78 of 134

Compiled by Navan Mudali

NicZenDezigns Page 79 of 134

Compiled by Navan Mudali

NicZenDezigns Page 80 of 134

Compiled by Navan Mudali

NicZenDezigns Page 81 of 134

Compiled by Navan Mudali

NicZenDezigns Page 82 of 134

Compiled by Navan Mudali

NicZenDezigns Page 83 of 134

Compiled by Navan Mudali

NicZenDezigns Page 84 of 134

November 2013

Compiled by Navan Mudali

NicZenDezigns Page 85 of 134

Compiled by Navan Mudali

NicZenDezigns Page 86 of 134

Compiled by Navan Mudali

NicZenDezigns Page 87 of 134

Compiled by Navan Mudali

NicZenDezigns Page 88 of 134

Compiled by Navan Mudali

NicZenDezigns Page 89 of 134

Compiled by Navan Mudali

NicZenDezigns Page 90 of 134

Compiled by Navan Mudali

NicZenDezigns Page 91 of 134

Compiled by Navan Mudali

NicZenDezigns Page 92 of 134

Compiled by Navan Mudali

NicZenDezigns Page 93 of 134

February 2014

Compiled by Navan Mudali

NicZenDezigns Page 94 of 134

Compiled by Navan Mudali

NicZenDezigns Page 95 of 134

Compiled by Navan Mudali

NicZenDezigns Page 96 of 134

Compiled by Navan Mudali

NicZenDezigns Page 97 of 134

Compiled by Navan Mudali

NicZenDezigns Page 98 of 134

November 2014

Compiled by Navan Mudali

NicZenDezigns Page 99 of 134

Compiled by Navan Mudali

NicZenDezigns Page 100 of 134

Compiled by Navan Mudali

NicZenDezigns Page 101 of 134

Compiled by Navan Mudali

NicZenDezigns Page 102 of 134

Compiled by Navan Mudali

NicZenDezigns Page 103 of 134

Compiled by Navan Mudali

NicZenDezigns Page 104 of 134

Compiled by Navan Mudali

NicZenDezigns Page 105 of 134

Compiled by Navan Mudali

NicZenDezigns Page 106 of 134

Compiled by Navan Mudali

NicZenDezigns Page 107 of 134

Compiled by Navan Mudali

NicZenDezigns Page 108 of 134

Compiled by Navan Mudali

NicZenDezigns Page 109 of 134

February 2015

Compiled by Navan Mudali

NicZenDezigns Page 110 of 134

Compiled by Navan Mudali

NicZenDezigns Page 111 of 134

Compiled by Navan Mudali

NicZenDezigns Page 112 of 134

Compiled by Navan Mudali

NicZenDezigns Page 113 of 134

Compiled by Navan Mudali

NicZenDezigns Page 114 of 134

Compiled by Navan Mudali

NicZenDezigns Page 115 of 134

Compiled by Navan Mudali

NicZenDezigns Page 116 of 134

Compiled by Navan Mudali

NicZenDezigns Page 117 of 134

November 2015

Compiled by Navan Mudali

NicZenDezigns Page 118 of 134

Compiled by Navan Mudali

NicZenDezigns Page 119 of 134

Compiled by Navan Mudali

NicZenDezigns Page 120 of 134

Compiled by Navan Mudali

NicZenDezigns Page 121 of 134

Compiled by Navan Mudali

NicZenDezigns Page 122 of 134

Compiled by Navan Mudali

NicZenDezigns Page 123 of 134

Compiled by Navan Mudali

NicZenDezigns Page 124 of 134

Compiled by Navan Mudali

NicZenDezigns Page 125 of 134

February 2016

Compiled by Navan Mudali

NicZenDezigns Page 126 of 134

Compiled by Navan Mudali

NicZenDezigns Page 127 of 134

Compiled by Navan Mudali

NicZenDezigns Page 128 of 134

Compiled by Navan Mudali

NicZenDezigns Page 129 of 134

Compiled by Navan Mudali

NicZenDezigns Page 130 of 134

Compiled by Navan Mudali

NicZenDezigns Page 131 of 134

November 2016

Compiled by Navan Mudali

NicZenDezigns Page 132 of 134

***** SOLUTIONS TO FOLLOW *****

Compiled by Navan Mudali

NicZenDezigns Page 133 of 134

February 2017

Compiled by Navan Mudali

NicZenDezigns Page 134 of 134

***** SOLUTIONS TO FOLLOW *****