# Chapter 13 (Alg 2) Flashcards

Distance formula

ⅆ=√((x_2−x_1 )^2+(y_2−y_1 )^2 )

The midpoint Formula

M=((x_1+x_2)/2,(y_1+y_2)/2)

Focus

A point that lies on the axis of symmetry, lies p amount from vertex

Directrix

A line Perpendicular to the axis of symmetry, lies p amount from vertex

Vertex

lies halfway between the focus and the directrix

Equation of parabola opening up or down with vetex (0,0)

x^2 = 4py

Parabolas opening to the left or right with vertex (0,0)

y^2 = 4px

Standard equation of a Parabola with Vertex at (0,0)

The standard form of the equation of a parabola with vertex at (0,0) is as follows: (the last one is axis of symm.)

x^2 = 4py, focus (0,p), Directrix y = -p, Vertical (x = 0)

y^2 = 4px, focus (p,0), Directrix x = -p, Horizon. (y = 0)

Circle

set of all points P in a plane that are equidistant from a fixed point, called the center

radius

distance between the center and any point on the circle

Standard Equation of a Circle with Center at (0,0)

The standard form of the equation ofa circle with center at (0,0) and radius r is as follows:

x^2 + y^2 = r^2

ellipse

the set of all points P in a plane such that the sum of the distances between P and two fixed points, called the foci, is a constant

major axis

The line segment joining the vertices of an ellipse

center of the ellipse

the midpoint of the major axis of an ellipse

co-vertices of an ellipse

The points of intersection of an ellipse and the line perpendicular to the major axis at the center