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 184
h the tangent is impossible. Thelimiting values may easily be shown to be the inclinations of per-pendiculars to the asymptotes. 245. We may now demonstrate properties of the hyperbola,analogous to those of the ellipse in Art. 194. First: . The sum of the squares of perpendiculars from the centre… … Since CRPR is a rectangle, the square of the diagonal is equal 180 THE HYPERBOLA. to the sum of the squares of two adjacent sides. Therefore CP2 —A2 — B2; that is, the distance of P from the centre is constant, andits locus is a circle whose radius is |/A2 — B2.* In the figure,A > B, and…
Geometry, Analytic
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