- parallel to y-axis, focus at (h, k + p): (x − h)^2 = 4p(y − k).
ELLIPSE
With major axis of length 2a, minor axis of length 2b, and distance between foci of 2c:
- Center at (0, 0), foci at (±c, 0), and vertices at (±a, 0):
- Center at (0, 0), foci at (0, ±c), and vertices at (0, ±a):
- Center at (h, k), major axis horizontal, and vertices at (h ± a, k):
- Center at (h, k), major axis vertical, and vertices at (h, k ± a):
For the ellipse, a^2 = b^2 + c^2 , and the eccentricity which is less than 1.
HYPERBOLA
With real (transverse) axis of length 2a, imaginary (conjugate) axis of length 2b, and distance
between foci of 2c:
- Center at (0, 0), foci at (±c, 0), and vertices at (±a, 0):
- Center at (0, 0), foci at (0, ±c), and vertices at (0, ±a):
- Center at (h, k), real axis horizontal, vertices at (h ± a, k):
- Center at (h, k), real axis vertical, vertices at (h, k± a):
