An elementary treatise on analytical geometry : embracing plane co-ordinate geometry, and an introduction to geometry of three dimensions (1869)
Johnson, William Woolsey, 1841-1927 · Philadelphia : J.B. Lippincott · leaf 108
right-angled triangle PRF, PR2 ===PF2 — FR2; but PF = PD = BR, and hence is represented byx -f- ip, and FR is x — \p; since BV and VF are each one-halfof BF or p. Therefore y2 = (x -j- ip)2 — (x — Jp)2, or expand-ing and reducing, y2 = 2px. The form of this equation shows that the curve passes… … 104 THE PARABOLA. parabola \ for this reason, VX is called the axis of the curve, and Ythe vertex. To indicate that the curve is referred to its axis andvertex, we may use X and Y in this equation. When the proper-ties of the parabola are investigated geometrically, the lines VRand PR are denned as…
Geometry, Analytic
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