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Find an equation for the hyperbola described.Graph the equation.

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Find an equation for the hyperbola described.Graph the equation.

Center at (- 3, - 4); focus at (- 3, - 8); vertex at (- 3, - 2)
asked Feb 3, 2015 in PRECALCULUS by anonymous
reshown Feb 3, 2015 by goushi

1 Answer

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Step 1:

The hyperbola center is at image, focus is at image and vertex is at image.

Observe the points, here coordinates are equal.

So, the hyperbola has a vertical transverse axis and its standard form of the equation is

.

Where,

is the center.

is the distance between center and vertex.

is the distance between center and focus.

.

The distance between center and vertex is image.

The distance between center and focus is image.

image

Substitute the values of in standard form of the equation.

image

Step 2:

The foci of the hyperbola is image.

The vertices of the hyperbola is image.

Find the points to form a rectangle.

image.

image.

The extensions of the diagonals of the rectangle are the asymptotes of the hyperbola

Asymptotes of the hyperbola are image.

Substitute the values of in image.

image

Asymptotes are image.

Step 3:

Graph :

(1) Draw the coordinate plane.

(2) Draw the equation of the hyperbola.

(3) Plot the center, foci and vertices.

(4) Form a rectangle containing the points image, image.

(5) Draw the asymptotes of the hyperbola.


image

Solution :

The equation of the hyperbola is image.

Graph of the hyperbola :

image

answered Feb 6, 2015 by joseph Apprentice

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