Understanding Hyperbolas and Eccentricity

x^2/a^2 - y^2/b^2 = 1

y^2/a^2 - x^2/b^2 = 1

x^2 - y^2 = 1

x^2 + y^2 = 1

(1/2, 0)

(0, 1)

(0, 1/2)

(1, 0)

Eccentricity is the sum of the distances to the foci

Eccentricity is the product of the distances to the foci

Eccentricity is the ratio of the distance to the focus over the distance to the directrix

Eccentricity is the distance to the directrix

Focal length is a^2 / b^2

Focal length is a^2 * b^2

Focal length is a^2 + b^2

Focal length is a^2 - b^2

a * eccentricity

a / eccentricity

eccentricity / a

a + eccentricity

3

1

2

1/2

c^2 + b^2 = m^2 * a^2

c^2 - b^2 = m^2 * a^2

c^2 * b^2 = m^2 + a^2

c^2 / b^2 = m^2 / a^2

Eccentricity is -1

Eccentricity is 2

Eccentricity is 1

Eccentricity is 0

Because it is defined as such

Because it is the ratio of distances

Because it is a property of parabolas

Because it is a property of ellipses

(epsilon^2 + 2)(epsilon^2 - 2)

(epsilon^2 - 2)(epsilon^2 - 2)

(epsilon^2 + 4)(epsilon^2 + 1)

(epsilon^2 - 4)(epsilon^2 - 1)