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 167
e hyperbola, take for the axis of X, thestraight line passing throughthe foci, F and F; and forthe axis of Y, a perpendicu-lar line bisecting FF. Letc denote the distance from,either focus to the origin;and 2A, the constant differ-ence of the lines PF andPF, or / and r, the focaldistances of the… … We have now to combine these three equations so as to derive anequation between x, y and the constants. From the first two we 2c,xhave /2 — r2 == 4cx; dividing by / — r = 2A, / -f- r = —-. AHence r = — 4- A A^ and ex r = A. A 162 THE HYPERBOLA. 163 Finally, substituting the value of / in the first…
Geometry, Analytic
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