7.2 Ellipses and Circles

Standard Form Equation (Horizontal)

Standard Form Equation (Horizontal)

(x-h)^2 / a^2 + (y-k)^2 / b^2 = 1

Standard Form Equation (Vertical)

(x-h)^2 / b^2 + (y-k)^2 / b^2 = 1

Center

(h, k)

Foci (Horizontal)

(h±c, k)

Vertices (Horizontal)

(h±c, k)

Co-vertices (Horizontal)

(h, k±b)

Major axis (Horizontal)

y=k

Minor Axis (Horizontal)

x=h

Foci (Vertical)

(h, k±c)

Vertices (Vertical)

(h, k±a)

Co-vertices (Vertical)

(h, k±b)

Major Axis (Vertical)

x=h

Minor axis (Vertical)

y=k

Relationship of a, b, and c

c = √a^2 - b^2

Standard Form Equation (Circle)

(x-h)^2 + (y-k)^2 = r