Mathematics and Society - OS X Lion Server

COMETS ANDCONICSECtIONS(PAGE. 3)2) A Method for Drawing Parabolasa) Draw a line t b) Using the page ofat the bottomof the sheetof paper.concentric circles,(see 1 (a) arrange acircle so it isChoose a point p tangent to line -e.P about 4 cmand passes throughQabove the line. point P. Mark itscenter on the paper.c) Repeat (b) with several differentsizes of circles. Connect thecenters with a smooth curve. Thecurve is a parabola.3) A Method for Drawing Hyperbolas(a) Draw a circle with .pa radius about 2 cm.Label its center C.Pick a point P outsidecircle C.b) Using the page ofconcentric circles,mark the centers ofseveral circles whichare tangent to circleC and pass through,,point P. Connect thecenters in a smoothI,,\\P~ .. ­curve.;;--;",-..-~-;::; ...." ''I" 'I , ,I , ', ,,"G, , ,c)poTrace circle Cand point P onanother sheet ofpaper.centers of circleswhich pass throughP, are tangent tocircle C and havecircle C "inside"them.Connect thecenters in a smooth curve~d) Put the two, curves together,,, ,, on the same.Csheet of paperas shown.Thisis a hyperbola.p... _--(116