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

Answer:

Step-by-step explanation:

x²/a² - y²/b² = 1

center (0,0)

vertex (3,0), so a = 3

focus (9,0)

e = 9/a = 3

directrices: x = ±a/e = ±1

Answer 2

The equations of the directrices with a vertex at (3, 0) and a focus of the hyperbola located at (9, 0) is x =  ±1.

What is the general equation of hyperbola?

The general equation of the hyperbola is in the form of

x²/a² - y²/b² = 1

We have been given center (0,0)

vertex (3,0),

so a = 3

focus (9,0)

So, e = 9/a = 3

The equation of directrices:

x = ±a/e = ±1

Hence, The equations of the directrices with a vertex at (3, 0) and a focus of the hyperbola located at (9, 0) is x =  ±1.

Learn more about hyperbola here:

brainly.com/question/4148030

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