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By A. C. Burdette (Auth.)

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Extra resources for Analytic Geometry

Example text

This does not require any definition of directions because a positive direction has already been assigned on the normal to a line. For example, we see in Figure 2-11 that dl is negative because it is measured opposite the positive direction on the normal. For similar reasons d2 is positive. In general, 38 2. THE STRAIGHT LINE , v, "V. Pi \ y \ l \ 0 Pi X P(x» yù Figure 2-11 Figure 2-12 if P and the origin are on opposite sides of the line, the directed distance will be positive ; if they are on the same side, it will be negative.

The application of the concept of symmetry to the problem of graphing an equation is obvious. 3-4. Extent A valuable aid in drawing the graph of an equation is knowledge of the extent of the curve, that is, what portion or portions of the plane are occupied by the curve. For example, it would help in drawing the graph if we knew the curve was entirely above the JC axis, or had no points in a strip of two-unit width on either side of the y axis, or was contained entirely within a certain rectangle.

10. 12. 14. 16. 18. 20. 22. 4 / - 9x2 = 36 x2 +y2 -2y = 0 x 2 + y2 - 6x = 0 xy + 2JC - y - 1 = 0 jcy2 = 12 x2y + x2 = 9y j e 2 / + 9x2 - 4y2 = 0 x2j> - 4y - 8 = 0 24.

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