8: Hooked on Conics
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In this chapter, we study the Conic Sections - literally 'sections of a cone'.
- 8.1: Introduction to Conics
- In this chapter, we study the Conic Sections - literally `sections of a cone'. We will focus the discussion on the non-degenerate cases: circles, parabolas, ellipses, and hyperbolas, in that order. To determine equations which describe these curves, we will make use of their definitions in terms of distances.
- 8.2: Circles
- Recall from Geometry that a circle can be determined by fixing a point (called the center) and a positive number (called the radius) as follows.
- 8.3: Parabolas
- We have already learned that the graph of a quadratic function is called a parabola. To our surprise and delight, we may also define parabolas in terms of distance in conics.
- 8.4: Ellipses
- This section covers the properties and equations of ellipses, focusing on their standard form, foci, vertices, and axes. It explains how to graph ellipses and determine key features like the center, major, and minor axes. Examples help illustrate how to identify and work with ellipses in various algebraic forms.
- 8.5: Hyperbolas
- This section explains the properties and equations of hyperbolas, focusing on their standard form, asymptotes, vertices, and foci. It describes how to identify and graph hyperbolas, distinguishing them from other conic sections. Examples demonstrate how to find key features and write equations for hyperbolas in various orientations.
Thumbnail: The circle and ellipse conic sections is determined by the angle the plane makes with the axis of the cone. The other two conic section (the hyperbola and parabolas) are not shown. (CC BY-SA 4.0; OpenStax)