# Chapter 10: Conics and Coordinate Geometry

**At Grade**Created by: CK-12

Here you will learn about the four conic sections: circles, parabolas, ellipses, and hyperbolas. You will focus on circles and parabolas and learn how to derive and use the equations of these conic sections. You will also review and extend algebra concepts relating to finding the lengths and slopes of lines in preparation for writing coordinate proofs.

- 10.1.
## Conic Sections

- 10.2.
## Equations of Circles

- 10.3.
## Equations of Parabolas

- 10.4.
## Slope of Parallel and Perpendicular Lines

- 10.5.
## The Distance Formula

- 10.6.
## Points that Partition Line Segments

- 10.7.
## Coordinate Proofs

### Chapter Summary

You learned that the conic sections are the cross sections of a double cone. There are four primary conic sections (the parabola, the circle, the ellipse, and the hyperbola) as well as three degenerate conics that are not as complex. You learned how to derive the equation of a circle using the Pythagorean Theorem and the equation of a parabola in terms of its focus and directrix.

Next you reviewed parallel and perpendicular lines from algebra. In particular, you proved that lines are parallel if and only if they have equal slopes and lines are perpendicular if and only if their slopes are opposite reciprocals.

You learned that the Pythagorean Theorem can be adapted to create the distance formula that allows you to find the distance between any two points. You also learned how to find the coordinates of a point that has partitioned a line segment in a given ratio.

Finally, you used both your algebra and geometry skills to practice writing coordinate proofs.

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