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Compiled by Navan MudaliAnalytical Geometry – Past Papers (Questions & Solutions)November 2008NicZenDezignsPage 1 of 134
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Compiled by Navan MudaliFebruary 2011QUESTION 4In the diagram below PQR with vertices P(– 1 ; 2), Q(– 2 ; – 2) and R(3 ; 0) is late the angle that PQ makes with the positive x-axis.(3)4.2Determine the coordinates of M, the midpoint of PR.(2)4.3Determine the perimeter of PQR to the nearest whole number.(5)4.4Determine an equation of the line parallel to PQ that passes through M.(3)[13]NicZenDezignsPage 37 of 134
Compiled by Navan MudaliQUESTION 55.15.2The equation of a circle isx 2 y 2 8 x 6 y 15 .5.1.1Prove that the point (2 ; – 9) is on the circu mference of the circle.(2)5.1.2Determine 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)[14]QUESTION 6The circle, with centre A and equation ( x 3) 2 ( y 2) 2 25 is given in the following diagram. B is ay-intercept of the circle.yBCxOA6.1Determine the coordinates of B.(4)6.2Write down the coordinates of C, if C is the reflect ion of B in the line x 3.(2)6.3The circle is enlarged through the origin by a factor of/3.2Write down the equation of the new circle, centre A , in the formNicZenDezigns( x a ) 2 ( y b) 2 r 2 .Page 38 of 134(2)
Compiled by Navan Mudali6.4In addition to the circle with centre A and equationcircle( x 12) 2 ( y 10) 2 100 with centre( x 3) 2 ( y 2) 2 25 , youare given theB.6.4.1Calculate the distance between the centres A and B.(2)6.4.2In how many points do these two circles intersect? Justify your answer.(2)[12]NicZenDezignsPage 39 of 134
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Compiled by Navan Mudali***** SOLUTIONS TO FOLLOWNicZenDezigns*****Page 132 of 134
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Compiled by Navan Mudali NicZenDezigns Page 38 of 134 QUESTION 5 5.1 The equation of a circle is x y2 8x 6y 15 5.1.1 Prove that t
