Plane Analytical Geometry

By M Bourne

The curves that we learn about in this chapter are called conic sections. They arise naturally in many situations and are the result of slicing a cone at various angles.

Depending on where we slice our cone, and at what angle, we will either have a straight line, a circle, a parabola, an ellipse or a hyperbola. Of course, we could also get a single point, too.

Why study analytic geometry?

Science and engineering involves the study of quantities that change relative to each other (for example, distance-time, velocity-time, population-time, force-distance, etc).

It is much easier to understand what is going on in these problems if we draw graphs showing the relationship between the quantities involved.

The study of calculus depends heavily on a clear understanding of functions, graphs, slopes of curves and shapes of curves. For example, in the Differentiation chapter we use graphs to demonstrate relationships between varying quantities.

In this Chapter

• 1. Distance Formula
• Gradient (Slope) of a Line, and Inclination
• Parallel Lines
• Perpendicular Lines
• 2. The Straight Line
• Perpendicular Distance from a Point to a Line
• 3. The Circle
• 4. The Parabola
• 5. The Ellipse
• 6. The Hyperbola
• 7. Polar Coordinates
• 8. Curves in Polar Coordinates
• Equi-angular Spiral

We begin with the Distance Formula »