# Ch.3 Coordinate Systems - Edexcel Maths FP1 Topic Questions...

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Leaveblank6*N34694A0628*3.The rectangular hyperbola,H, has parametric equationsx= 5t,y=5t,t0.(a) Write the cartesian equation ofHin the formxy=c2.(1)PointsAandBon the hyperbola have parameterst =1 andt= 5 respectively.(b) Find the coordinates of the mid-point ofAB.(3)_______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________January 2009physicsandmathstutor.com
Leaveblank16*N34694A01628*8.A parabola has equationy2= 4ax,a> 0. The pointQ(aq2,2aq) lies on the parabola.(a) Show that an equation of the tangent to the parabola atQisyq=x+aq2.(4)This tangent meets they-axis at the pointR.(b) Find an equation of the linelwhich passes throughRand is perpendicular to thetangent atQ.(3)(c) Show thatlpasses through the focus of the parabola.(1)(d) Find the coordinates of the point wherelmeets the directrix of the parabola.(2)_____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________January 2009physicsandmathstutor.com
Leaveblank16*M35146A01624*6.The parabolaChas equationy2= 16x.(a) Verify that the pointP(4t2, 8t) is a general point onC.(1)(b) Write down the coordinates of the focusSofC.(1)(c) Show that the normal toCatPhas equationy+tx= 8t+ 4t3(5)The normal toCatPmeets thex-axis at the pointN.(d) Find the area of trianglePSNin terms oft, giving your answer in its simplest form.(4)________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________June 2009physicsandmathstutor.com
Leaveblank8*N35143A0824*4.BPASxyy2=12xFigure 1Figure 1 shows a sketch of part of the parabola with equationy2=12x.The pointPon the parabola hasx-coordinate13.The pointSis the focus of the parabola.(a) Write down the coordinates ofS.(1)The pointsAandBlie on the directrix of the parabola.The pointAis on thex-axis and they-coordinate ofBis positive.Given thatABPSis a trapezium,(b) calculate the perimeter ofABPS.(5)______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________January 2010physicsandmathstutor.com
Leaveblank14*N35143A01424*7.The rectangular hyperbolaHhas equationxyc=2, wherecis a constant.The pointP ctct,is a general point onH.(a) Show that the tangent toHatPhas equationt yxct22+=(4)The tangents toHat the pointsAandBmeet at the point (15c, –c).(b) Find, in terms ofc, the coordinates ofAandB.(5)______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________January 2010physicsandmathstutor.com
Leaveblank12*N35387A01228*5.The parabolaChas equation220 .yx(a) Verify that the point2(5,10 )Pttis a general point onC(1)The pointAonChas parameter4.The linelpasses throughAand also passes through the focus of(b) Find the gradient ofl=.t=C..(4)_______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________June 2010physicsandmathstutor.com
Leaveblank20*N35387A02028*8.The rectangular hyperbolaHhas equation2,xyc=where c is a positive constant.The pointAonHhasx-coordinate 3(a) Write down they-coordinate ofAc..(1)(b) Show that an equation of the normal toHatA32780yxc=(5)The normal toHatAmeetsHagain at the point(c) Find, in terms ofc, the coordinates ofBisB..(5)________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________June 2010physicsandmathstutor.com
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