Loney, S. L. (Sidney Luxton), 1860-1939 · London, Macmillan and co. · leaf 211
the curve. Let PVX be the diameter and PY the tangent at Pmeeting the axis in T. Take any point Q on the curve,and draw QM perpendicular to theaxis meeting the diameter P F in L. Let PVhQ X and VQ be y.Draw PN perpendicular to theaxis of the curve, and let e^ /. YPX=iPTM,Then iAS. A]S[^PN^ = ]SfT^… … THE PARABOLA. EXAMPLES. 197 Substituting these values in (1), we have (2a cot 0 + y sin Oy — ia (a cot^ 0 + x + y cos 6), i. e. if- sin^ 6 — ^ax. The required equation is therefore y^^lpx (2), where p - T^= « (1 + ^ot Q) = a^ AN= SP (by Art. 202). The equation to the parabola referred to the above…
Coordinates · Geometry, Analytic
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