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Find the center, vertices, foci, and the equations of the asymptotes of the hyperbola.

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Find  the  center,  vertices,  foci,  and  the equations of the asymptotes of the hyperbola. Use a graphing utility to graph the hyperbola and its asymptotes.

2x^2 - 3y^2 = 6
asked Feb 2, 2015 in TRIGONOMETRY by anonymous

1 Answer

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Step 1:

The equation is image.

image

image

Compare it to the standard form of the hyperbola .

Here transverse axis is parallel to the axis.

is the center of the hyperbola.

image

image

image

is the distance between center and focus.

.

Step 2:

The center of the hyperbola is image.

The vertices of the hyperbola are image.

The foci of the hyperbola are 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 .

Substitute the values of in .

image

Asymptotes are image.

Step 3:

Graph :

(1) Draw the coordinate plane.

(2) Draw the equation of the hyperbola.

(3) Plot the foci and vertices.

(4) Form a rectangle containing the points image.

(5) Draw the asymptotes of the hyperbola.

 image

Solution :

The center of the hyperbola is image.

The vertices of the hyperbola are image.

The foci of the hyperbola are image.

Asymptotes of the hyperbola are image.

Graph of the hyperbola and asymptotes :

image

answered Feb 7, 2015 by joseph Apprentice

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