...are taken for axes, assumes the more simple form :, 1 . (6), .. _ _-. From these expressions for y and x, it appears that for the same value of x, there...for x = A, or x — — A, the corresponding value of y is 0, it follows that parallels to the axis of y drawn through the points B, A, of the curve,...

...are taken for axes, assumes the more simple form ^,;f_J . (6), g A AB From these expressions for y and x, it appears that for the same value of x, there...since, for x = A, or x = — A, the corresponding value of y is 0, it follows that parallels to the axis of y drawn through the points B, A, of the curve,...

...imaginary. Therefore no point on the parabola is situated on the left of the origin. For every positive value of x there are two values of y, numerically equal, but contrary in sign. This implies that for every point above the axis of x there is a corresponding point...

...stated. We see from equation (1), that for every value of x, corresponding to points of the curve, there are two values of y, numerically equal, but having contrary signs; this shows that the curve is symmetrical with respect to the axis of x. Solving equation [27] with...

...between A and A'. If x be supposed a greater magnitude than +i* or — a, then (1) shews that for every value of x there are two values of y, numerically equal, but contrary in sign. This implies that, for every point above the axis of z, there is a corresponding...

...y is imaginary. Therefore no points of the locus lie to the left of the ;/-axis. For every positive value of x there are two values of y numerically equal but opposite in sign. Hence the two corresponding points of the locus are equidistant from the x-axis....

...hence the curve opens to the right or to the left according as a is positive or negative. For every value of x there are two values of y. numerically equal but of opposite sign, which grow larger as x grows larger: the curve is an open curve extending to infinity...