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?

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asked Oct 23, 2024 170k views

1 Answer

Swanson · Answer 1 · 2024-10-30T14:28:54+0000

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

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.