Conic Sections

Question 1

Ellipse

Answer 1

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

or

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

2a is the length of the major axis, sqrt(a^2 - b^2) make the foci, (h,k) is the center.

Question 1

Hyperbola

Answer 1

(x-h)^2/a^2 - (y-k)^2/b^2 = r^2
(Asymptotes y=b/ax and y=-b/ax)

or

(y-k)^2/a^2 - (x-h)^2/b^2 = r^2
(Asymptotes y=a/bx and y=-a/bx)

2a is the length of the major axis, sqrt(a^2 + b^2) make the foci, (h,k) is the center.

Question 2

Parabola

Answer 2

y^2 = 4px
(Horizontal)

or

x^2 = 4py
(Vertical)