Question

A hyperbola centered at the origin has a vertex at (3, 0) and a focus of the hyperbola is located at (9, 0). What are the equations of the directrices?
x = ±

Answer 1

the answer is 1.,.....

Answer 2

The equations of the directrices with a vertex at (3, 0) and a focus of the hyperbola is located at (9, 0) is x = -3

How to determine the equation of directrices given vertex and focus?

The standard coordinate of the focus is (h + p, k) and the directrix is x = h - p.

Given the following parameters

vertex = (3, 0)

focus = (9, 0)

Equating the coordinates

9 = h + p

h = 3 (from the vertex)

9 = 3 + p
p = 9 - 3

p = 6

Determine the equation of the directrices

x = h - p

x = 3 - 6
x = -3

Hence the equations of the directrices with a vertex at (3, 0) and a focus of the hyperbola is located at (9, 0) is x = -3

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