Schaum's Outline of Theory and Problems of Beginning Calculus

CHAP. 3) GRAPHS OF EQUATIONS 17on completing the squares; that is, replacing the quantities x2 + Ax and y2 + By by the equal quantitiesA2 and (y+:)’-~ B2EXAMPLE Let us find the graph of the equationx2+y2+4x-2y+ 1 = oCompleting the squares, replace x2 + 4x by (x + 2)2 - 4 and y2 - 2y by (y - 1)2 - 1,(x+2)2-4+(y-1)2-1+1=o(x + 2)2 + (y - 1)2 = 4This is the equation of a circle with center (- 2, 1) and radius 2.Solved Problems3.1 Find the graph of: (a) the equation x = 2; (b) the equation y = -3.(a) The points satisfying the equation x = 2 are of the form (2, y), where y can be any number. Thesepoints form a vertical line [Fig. 3-6(a)].(6) The points satisfying y = -3 are of the form (x, -3), where x is any number. These points form ahorizontal line [Fig. 3-6(6)].0000000:F 2I0Fig. 3-6...... ..............-3 t3.2 Find the graph of the equation x = y2.Plotting several points suggests the curve shown in Fig. 3-7. This curve is a parabola, which may beobtained from the graph of y = x2 (Fig. 3-2) by switching the x- and y-coordinates.