Analytic geometry for colleges, universities, and technical schools (1892)
Nichols, E. W. (Edward West), 1858- · Boston [Mass.] : Leach, Shewell & Sanborn · leaf 204
th the perpendicularOP let fall from its vertex upon the tangent drawn at T asthe point of tangency moves around the curve. 1. To deduce the rectangular equation. Let T {x, y) be the point of tangency, and let P (cc, 3/)be a point of the curve. Let y^ = 4: px be the equation of the common parabola.… … Fig. 59. Since TT is parallel to OY, we have for its equation x=x . . . (2)Combining (1) and (2), we have y = - _ y p But hence y = V4:2)x ; V4 px „ y = —^ • X . 2 p Squaring and dropping accents, we have 2/^ = ^ . . . (3)Pfor the equation of the semi-cubic parabola. This curve is remarkable as…
Geometry, Analytic
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