Example 2.12. The transformation w = maps lines onto lines or parabolas.

(a) Find the image of the vertical line x = a.

Hence, the image of the vertical line x = a is a parabola.

(b) Find the image of the horizontal line y = b.

Hence, the image of the horizontal line y = b is a parabola.

The two families of parabolas are shown in the figure below.

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 (c) John Mathews, 1998, 2006