Conics are figures or shapes that are realized by slicing a cone at different angles. Go to the following website to see a good representation of the slicing of a cone, a short mathematical history of conics, and several examples of conics in the real world and their uses.

The Occurrence of Conics
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In this lesson, you will master the graphing of an ellipse when given the equation of an ellipse - in any form. You will understand the changes in the values of the coefficients and constants in the equation and how those changes are represented on the graph.

The standard form of any conic section is Ax² + Bxy + Cy² + Dx + Ey + F = 0, where A, B, C, D, E, and F are real numbers.

To form an ellipse, it must be true that A and C are both positive and A ≠ C. This is what makes an ellipse different from a circle. See Module 3, Lesson 11 to review circles.

The “graph” form of the equation of an ellipse is: x minus h squared over r sub x squared (x − h)² (r_x)² + y minus k squared over r sub y squared (y − k)² (r_y)²

• The point (h, k) is the center of the ellipse
• r_xis the radius in the x-direction and r_y is the radius in the y-direction
• The larger of the x-radius or y-radius is the radius of the major axis (also referred to as “a”)
• The shorter of the x-radius or y-radius is the radius of the minor axis (also referred to as “b”)