# Circles

## 10 terms

(h,k)

### standard form equation of a circle

r squared = (x-h) squared + (y-k) squared

### standard form of an equation of a circle if the center of the circle is the origin

x squared + y squared = r squared

### standard form of an equation of a circle if the center is a unit circle

x squared + y squared = 1

### general form of an equation of a circle

x squared + y squared + Dx + Ey = -F

### further expanded general form of an equation of a circle

x squared + Dx + (D/2) squared + y squared + Ey + (E/2) squared = -F + (D/2) squared + (E/2) squared

### How do you complete the square?

take half the middle term's coefficient, square it, and add that to both sides

### How do you plot a circle?

Plot the center, and count out the distance of the circle's radius directly above, below, left, and right of the point.

### How do you find the equation of a circle given three points

Plug in each coordinate pair into the general form. Then use a matrix to solve for D, E, and F. Then plug those variables back in to a blank general form (leaving x and y in variable form.)

### How do you transfer an equation to standard form from general form and visa versa?

Complete the square and simplify.