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 161
2x2-{- 3/+ 6x — 4 = 0; of x2 -j- y2 -j- 2x — 2y -f * The equation of the ellipse referred to a diameter and tangent isR2 R2 R2 R2 rf. r, y2 + — x2 = 2 — x. Put — = p, then — = A and y2 +^x2 = 2px.A2 A A A2 A A B2 p Let p remain constant, and A and B increase without limit, then — — — A2 A decreases… … 1 = 0 with 2x2 + 2y2 — 4x — 4y-f-2 = 0; of 3x2 + y2 — 6x = 8with 2/ = 12x — 6x\ 214. If the ellipses touch one another, the straight line will bea common tangent, as AB inthe figure, the two points of in-tersection coinciding at P. JoinP to the centres, 0 and C,then CP and OP are semi-di-ameters of…
Geometry, Analytic
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