Algebra and Trigonometry, 5th Edition

10.2 The Circle and the Ellipse

• Given an equation of a circle, complete the square, if necessary, and then find the center and the radius and graph the circle.

• Given an equation of an ellipse, complete the square, if necessary, and then find the center, the vertices, and the foci and graph the ellipse.

Circles

We can define a circle geometrically.

Circle

A circle is the set of all points in a plane that are at a fixed distance from a fixed point (the center) in the plane.

CIRCLES

REVIEW SECTION 1.1

Recall the standard equation of a circle with center (h, k) and radius r.

Standard Equation of a Circle

The standard equation of a circle with center (h, k) and radius r is

$${(x-h)}^2+{(y-k)}^2=r^2.$$

Example 1

For the circle

$$x^2+y^2-16x+14y+32=0$$