C - Circles Lesson

Circles

A conic section is formed by the intersection of a right circular cone and a plane. We will explore four conic sections: circles, parabolas, ellipses, and hyperbolas.  

Our goal is to graph these shapes on a coordinate plane.

First, we are going to review circles. You may remember that the standard form for a circle is:

$\left(x-h\right)^2+\left(y-k\right)^2=r^2$

where (h, k) is the center and r is the radius

A circle is the set of all points equidistant from a given point, called the center.

Let's see if you can use that formula to match the following:

Recall the midpoint and distance formulas:

        Midpoint: $\left(\frac{x_1+x_2}{2},\:\frac{y_1+y_2}{2}\right)$       Distance: $\sqrt[]{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}$

 

You should be able to use these formulas and properties you know about circles to write the equation of a circle given some information. Let's see some problems worked out.

A conic equation in general form can look something like the following:

$Ax^2+Cy^2+Dx+Ey+F=0$

This may look scary, but throughout the module we will learn which type of conic is represented by a given equation. For now, let's be sure you know how to convert that form to a circle. Watch this video to see how.

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