8.3 Hyperbolas

Standard Equation (Center (0, 0) with focal x-axis)

x²/a² - y²/b² = 1

Foci (Center (0, 0) with focal x-axis)

(±c, 0)

Vertices (Center (0, 0) with focal x-axis)

(±a, 0)

Asymptotes (Center (0, 0) with focal x-axis)

y = ±b/a*x

Standard Equation (Center (0, 0) with focal y-axis)

y²/a² - x²/b² = 1

Foci (Center (0, 0) with focal y-axis)

(0, ±c)

Vertices (Center (0, 0) with focal y-axis)

(0, ±a)

Asymptotes (Center (0, 0) with focal y-axis)

y = ±a/b*x

Standard Equation (Center (h, k) with focal axis y = k)

(x - h)²/a² - (y - k)²/b² = 1

Foci (Center (h, k) with focal axis y = k)

(h±c, k)

Vertices (Center (h, k) with focal axis y = k)

(h±a, k)

Asymptotes (Center (h, k) with focal axis y = k)

y = ±b/a(x - h) + k

Standard Equation (Center (h, k) with focal axis x = h)

(y - k)²/a² - (x - h)²/b² = 1

Foci (Center (h, k) with focal axis x = h)

(h, k±c)

Vertices (Center (h, k) with focal axis x = h)

(h, k±a)

Asymptotes (Center (h, k) with focal axis x = h)

y = ±a/b(x - h) + k

Transverse Axis (all)

2a

Conjugate Axis (all)

2b

Pythagorean Relation (all)

c² = a² + b²