Loney, S. L. (Sidney Luxton), 1860-1939 · London, Macmillan and co. · leaf 236
ifn ** _ial bm 243. To find the focus of the j^arabola a W h Let ^S be the focus, 0 the origin, and P and Q thepoints of contact of the parabola with the axes. Since, by Art. 230, the triangles OSP and QSO aresimilar, the angle SOP- angle SQO. Hence if we describe a circle through 0, Q, and S,… … P X The equation to this circle is x^ + 2xy cos oi +y^ = by (1). Similarly, since z SOQ — L SPO^ S will lie on the circlethrough 0 and P and touching the axis of y at the origin,i.e. on the circle x^ + 2xy cos (0 +y^ — ax (2). The intersections of (1) and (2) give the point required.On solving (1)…
Coordinates · Geometry, Analytic
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