# Unit 11: Chapter 18 - Circles and Parabolas

## Circles

**Definition:** The set of all points in a plane equal distance from a fixed point called the center.

**General form:** * Ax*^{2} + Cy^{2} + Dx + Ey + F = 0

**Standard form:** * (x - h)*^{2} + (y - k)^{2} = r^{2}

**center:** (h, k)

**radius:** *r*

### Testing if a point is on, inside, or outside a circle

#### using the equation of a circle:

- plug in the point in question
- compare to r
^{2}...
- = means on the circle
- > means outside the circle
- > means inside the circle

### Finding Symmetric Points

Use the lines x = h and y = k as lines of symmetry. (remember that vertex is (h, k)

## Parabolas

**Definition:** The set of all points in a plane equal distance from a fixed point called the focus and a fixed line called the directrix.

p is the distance (with direction) between the vertex and the focus or opposite the directrix

p = ^{1}⁄_{4a}

General formVertex form
* Ax*^{2} + Dx + Ey + F = 0 |
* Cy*^{2} + Dx + Ey + F = 0 |

y = a(x - h)^{2} + k |
x = a(y - k)^{2} + h |

vertex: (h, k) |
vertex: (h, k) |

*watch out (remember to reverse k and h for horizontal parabola's vertex) |

In circles, A = C, and both are not equal to 0. In parabolas, A = 0 or C = 0.