170k views
3 votes
The hyperbola has vertices at (-1, -5) and (11, -5), and its asymptote is the line y+5 = 7/6(x-5). What is the equation of the hyperbola in standard form?

User Nachos
by
8.7k points

1 Answer

5 votes

Final answer:

To find the equation of the hyperbola in standard form, determine the center, calculate the distances, and write the equation using the values.

Step-by-step explanation:

To find the equation of the hyperbola in standard form, we first need to determine the center of the hyperbola.

The center is the midpoint between the vertices, which is (-1+11)/2 = 5.

Next, we need to determine the distance between the center and vertices.

The distance is the absolute value of the difference in the x-coordinates or y-coordinates, so the distance is |11-5| = 6.

Now we can write the equation of the hyperbola in standard form:

(x-5)^2/a^2 - (y+5)^2/b^2 = 1

where a is the distance between the center and vertices, and b is the distance between the center and the asymptotes.

User Swanson
by
9.1k points