Reduce to the canonical form the below equation

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Give the detailed description of the curve.

Solution: Complete the perfect squares.

.

Now divide both sides by number 8 to obtain the equation

,

which corresponds to the hyperbola with the center at the point (3, -2). The focuses are located on the horizontal line y = -2. The distance between each focus and the center of the hyperbola is

.

The eccentricity of the hyperbola equals