Loney, S. L. (Sidney Luxton), 1860-1939 · London, Macmillan and co. · leaf 347
9. To trace the parabola given by the general equa-tion of the second degree a^ + 2hxy + blf + 2^cc + yy + c = 0 (1), and to find its latus rectum. First Method. Since the curve is a parabola wehave A^ = ab, so that the terms of the second degree forma perfect square. Put then a — c^ and 6 = yS^,… … We have therefore to turn the axes through an angle 0 /8 such that tan ^ = — —, and therefore sin 0 = — Va2 + ^2 and cos 6 = sJa^ + P TRACING OF PARABOLAS. 333 For X we have to substitute JT cos 0 — Fsin 0, i. e. , Ja + ftand for y the quantity JTsin^ + Tcos^, i.e. ---^+1^^ (Art. 129.) For ax + Py…
Coordinates · Geometry, Analytic
Internet Archive · Boston College Libraries · Public Domain Mark 1.0. Free to use for anything.
