Question

How to find the equation of a hyperbola when given the vertices and foci

Answer 1

To find the equation of a hyperbola when given the vertices and foci, use the standard form of the equation for a hyperbola and substitute the coordinates of the vertices and foci.

Step-by-step explanation:

To find the equation of a hyperbola when given the vertices and foci, you will need to use the standard form of the equation for a hyperbola. The equation for a hyperbola with vertical transverse axis is:

(y - k)^2 / a^2 - (x - h)^2 / b^2 = 1

where (h, k) represents the center of the hyperbola, a is the distance from the center to the vertices, and b is the distance from the center to the foci.

By substituting the given coordinates of the vertices and foci, you can determine the specific equation of the hyperbola.

Answer 2

Step-by-step explanation:

The vertices and foci are on the x-axis. Thus, the equation for the hyperbola will have the form x2a2−y2b2=1 x 2 a 2 − y 2 b 2 = 1 . The vertices are (±6,0) ( ± 6 , 0 ) , so a=6 a = 6 and a2=36 a 2 = 36 . The foci are (±2√10,0) ( ± 2 10 , 0 ) , so c=2√10 c = 2 10 and c2=40 c 2 = 40 .