Higher geometry; an introduction to advanced methods in analytic geometry (1922)
Woods, Frederick S. (Frederick Shenstone), 1864- · Boston, New York, Ginn and Company · leaf 111
the conic (1) asA, and the tangent to (1) at A as AB. s*The equation of (1) then isx?+2x^=0, while that of (2), since it is knownonly to be tangent to BC at C, is ajcl + a^ + 2 a^c,2xs + 2 aix^cx= 0.The collineation (3) is then of the type pxa =j _ &.Xa. px2 = a,x2+ afa, px[ = atxt + asx2 +… … Fig. 32 LINEAR TRANSFORMATIONS 99 If this point is taken as the point A in the coordinate triangle,we have «a = 0. The equations of the conies are then x%+2x1xs=Q, (13) x\ + 2 aax2xa + 2 X& = 0, (14) and the collineation (3) is px[ = x1 + ctax2 = ax1 + x2, px2 = x2 + aaxs = ax2 + xs, (15) pxa =…
Geometry, Analytic
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