Chapter 22. Analytic Geometry

OBJECTIVES

When you have completed this chapter, you should be able to

  • Calculate the distance between two points.

  • Determine the slope of a line given two points on the line.

  • Find the slope of a line given its angle of inclination, and vice versa.

  • Determine the slope of a line perpendicular to a given line.

  • Calculate the angle between two lines.

  • Write the equation of a line using the slope-intercept form, the point-slope form, or the two-point form.

  • Solve applied problems involving the straight line.

  • Write the equation of a circle, ellipse, parabola, or hyperbola from given information.

  • Write an equation in standard form given the equation of any of the previous curves.

  • Determine all the features of interest from the standard equation of any of these curves.

  • Make a graph of any of these figures.

  • Tell, by inspection, whether a given second-degree equation represents a circle, ellipse, parabola, or hyperbola.

  • Write a new equation for a curve with the axes shifted when given the equation of that curve.

  • Solve applied problems involving any of these figures.

Here we start our study of analytic geometry. This is a branch of mathematics in which geometric figures such as points, lines, and circles are placed on the same coordinate axes we introduced in our chapter on graphing. This enables us to write an equation for each geometric figure. That equation can then be analyzed and manipulated using algebra to give us more information about the geometric figure than was ...

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