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Analytical Geometry – Past Papers (Questions & Solutions)
November 2008
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QUESTION 4
In the diagram below  PQR with vertices P(– 1 ; 2), Q(– 2 ; – 2) and R(3 ; 0) is given.
y
5
4
3
P
2
1
-4
-3
-2
-1
x
R
O
-5
1
2
3
4
5
-1
Q
-2
-3
-4
-5
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)
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QUESTION 5
5.1
5.2
The equation of a circle is
x 2  y 2  8 x  6 y  15 .
5.1.1
Prove that the point (2 ; – 9) is on the circu mference of the circle.
(2)
5.1.2
Determine an equation of the tangent to the circle at the point (2 ; – 9).
(7)
Calculate the length of the tangent AB drawn from the point A(6 ; 4) to the circle with equation
( x  3) 2  ( y  1) 2  10 .
(5)
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QUESTION 6
The circle, with centre A and equation ( x  3) 2  ( y  2) 2  25 is given in the following diagram. B is a
y-intercept of the circle.
y
B
C
x
O
A
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
/
3
.
2
Write down the equation of the new circle, centre A , in the form
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( x  a ) 2  ( y  b) 2  r 2 .
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6.4
In addition to the circle with centre A and equation
circle
( x  12) 2  ( y  10) 2  100 with centre
( x  3) 2  ( y  2) 2  25 , you
are given the
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)
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***** SOLUTIONS TO FOLLOW
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*****
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*****
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SOLUTIONS TO FOLLOW
*****
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