CO3 - Analytic Geometry and Conic Sections

Equations of Lines, Circles, Conic Sections: Parabola, Ellipse, Hyperbola

straight line

shortest path between two points

Standard Form of Line

slope

measure of steepness

inclination

Positive angle measured counterclockwise from the x-axis to a nonhorizontal line

m=tanθ

If a nonvertical line has inclination θ and slope m

Slope of a Line

x-intercept

Point where line intersects with the x-axis

y-intercept

Point where line intersects with the y-axis

Slope-Intercept Form

Point-Slope Form

Two-point Form

parallel lines

Lines with equal slopes

perpendicular lines

The slope of one line is the negative reciprocal of the other.

perpendicular lines

Finding the distance between a line and a point not on the
line is an application of __________.

Distance Between a Line and a Point

circle

a set of points that are equidistant from a fixed point, C(ℎ, 𝑘)

center

C(ℎ, 𝑘)

radius

The fixed distance 𝑟 from the center to any point on the circle

Standard Form of the Equation of a Circle

Equation of a Circle Centered at the Origin

General Equation of a Circle

conics

Curve obtained from a cone’s surface intersecting a plane

conic sections

Parabolas, Ellipses, Hyperbolas

parabola

The set of points in a plane that are equidistant from a fixed line, the directrix, and a fixed point, the focus, not on the directrix

axis of symmetry of the parabola

The line that passes through the focus and is perpendicular to the directrix

vertex of the parabola

The midpoint of the line segment between the focus and the directrix on the axis of symmetry

vertex of the parabola

The midpoint of the line segment between the focus and the directrix on the axis of symmetry

latus rectum

The line segment that passes through the focus and is parallel to the directrix, and with endpoints on the parabola

ellipse

The set of all points in a plane such that the sum of the distances of P from two fixed points and of the plane is constant.