How do you find the standard equation of a hyperbola given the foci?

How To: Given the equation of a hyperbola in standard form, locate its vertices and foci.

1. Solve for a using the equation a=√a2 a = a 2 .
2. Solve for c using the equation c=√a2+b2 c = a 2 + b 2 .

How do you solve a hyperbola equation in standard form?

The graph of a hyperbola is completely determined by its center, vertices, and asymptotes. The center, vertices, and asymptotes are apparent if the equation of a hyperbola is given in standard form: (x−h)2a2−(y−k)2b2=1 or (y−k)2b2−(x−h)2a2=1.

How do you find the standard equation of a hyperbola?

Standard Equation of Hyperbola. The equation of the hyperbola is simplest when the centre of the hyperbola is at the origin and the foci are either on the x-axis or on the y-axis. The standard equation of a hyperbola is given as: [(x 2 / a 2) – (y 2 / b 2)] = 1. where , b 2 = a 2 (e 2 – 1)

How do you find the foci of a hyperbola?

The hyperbola is centered at the origin, so the vertices serve as the y -intercepts of the graph. To find the vertices, set x = 0 x = 0, and solve for y y. The foci are located at ( 0, ± c) ( 0, ± c).

How do you find the transverse axis of a hyperbola?

Identify the vertices and foci of the hyperbola with equation y2 49 − x2 32 =1 y 2 49 − x 2 32 = 1. The equation has the form y 2 a 2 − x 2 b 2 = 1 y 2 a 2 − x 2 b 2 = 1, so the transverse axis lies on the y -axis. The hyperbola is centered at the origin, so the vertices serve as the y -intercepts of the graph.

What are the most important terms related to hyperbola?

Some of the most important terms related to hyperbola are: 1 Eccentricity (e): e 2 = 1 + (b 2 / a 2) = 1 + [ (conjugate axis) 2 / (transverse axis) 2] 2 Focii: S = (ae, 0) & S′ = (−ae, 0) 3 Directrix: x= (a/e), x = (−a / e) 4 Transverse axis: More