Circles and Ellipses

These flashcards cover essential vocabulary related to circles and ellipses, including their equations, properties, and standard forms.

Circle Equation

(x-n)² + (y-k)² = p² represents the standard form of a circle.

Ellipse Center

The center of an ellipse is denoted by the coordinate (h, k).

Major Axis

The longer diameter of the ellipse, represented by 'a' (the radius of the major axis).

Minor Axis

The shorter diameter of the ellipse, represented by 'b'.

Foci (Foci Location)

Foci are located at (h, k±c) for vertical ellipses and (h±c, k) for horizontal ellipses.

c² = a² - b²

This equation is used to find 'c', the distance from the center to each focus of the ellipse.

Vertical Ellipse

An ellipse that opens up and down, where the major axis is vertical.

Horizontal Ellipse

An ellipse that opens left and right, where the major axis is horizontal.

Co-vertex

The points on the ellipse that are perpendicular to the vertices, located at (h±b, k) for horizontal.

Standard Form of an Ellipse

Written as (x-h)²/a² + (y-k)²/b² = 1, where 'a' is the semi-major axis and 'b' is the semi-minor axis.