Woods, Frederick S. (Frederick Shenstone), 1864-, Bailey, Frederick H. (Frederick Harold), 1865- · Boston, New York [etc.] Ginn and Company · leaf 51
34 GRAPHS OF ALGEBRAIC FUNCTIONS Ex. 9. Find the points of intersection of 2 x2 + 3 y* = 35 (1) and xy = 6. (2) Since these equations are homogeneous quadratic equations, we place y = mx (3) and substitute for y in both (1) and (2). The results are 2 a;2 + 3 ra2x2 = 35 and mx2 = 6, whence x2- 35… … 2 + 3 m2 m v from which we find m = % or f.If m= i) then, from (5), x=±2;and from (3) the correspondingvalues of y are ± 3. If m = §, in like manner wefind x = ± \ ^Q and y = ± 1V6. Therefore the curves intersect at the four symmetrically situatedpoints (2, 3), (- 2, - 3), (3 Vo, 2 Vo), (- 1 Vti, -…
Geometry, Analytic · Calculus
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