Ziwet, Alexander, 1853-1928, Hopkins, Louis Allen, joint author · New York, The Macmillan company · leaf 116
of the circle. Similarly, in a parabola, the locus of the midpoints of all chordsparallel to any given direction is a straigM line, and this linewhich is parallel to the axisis called a diameter of theparabola. To prove this, takethe vertex as origin and theaxis of the parabola as axis Ox(Fig. 60)… … r 4a , 4a6 „ ■ — y-\ = 0. m m 106 PLANE ANALYTIC GEOMETRY [VI, § 105 The roots y^, y^ are the ordinates of the points Pi, Pj ^•twhich the line intersects the parabola. The sum of the roots is 4a 2/1 + 2/2 =—; m hence the ordinate \{yi + y^ of the midpoint P between Pj, Pjis constant {i.e.…
Geometry, Analytic
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