Plane and solid analytic geometry; an elementary textbook (1905)
Ashton, Charles H. (Charles Hamilton), 1866- · New York, C. Scribner's Sons · leaf 112
of chords whichpass through a fixed point {x^, y^ of the circle x^ -^ y^ = r^. Let P, (x\ y^ihe the middle point of any chord throughP^, (rzi, ^i). Let {x^.y^ be the coordinates of P^^ theother extremity of the chord. From the formulas for bisecting a line [4], we have (1) ^=^_X+£2, and (2) y =… … 90 ANALYTIC GEOMETRY [Cu. VIII, § 01 to eliminate the parameters and obtain a single equationin terms of the variables and constants only. Solving (1)and (2) for x^ and y^, we have x^ = 2x -x^, and ij^ = 2i/ Vv Substituting these values in (3), we have 4^2 4. 4^2 _ 4:ria; - 4 t/^ + x^^ + y^^ = r\ ■…
Geometry, Analytic
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