Precalculus 2014
67

 PAGE: 451 SET: Exercises PROBLEM: 67

Observe the graph:

The hyperbola is horizontal.

Standard form of hyperbola is , where is center.

Vertices: .

Foci: .

Asymptotes: .

.

The center of the hyperbola located at .

The vertices of the hyperbola is .

Therefore, and .

Find the value of .

The point is lies on the hyperbola.

By the definition of the hyperbola, the absolute value of the differences from any point on the hyperbola to the foci is constant.

.

Let and and .

Substitute the corresponding values in .

Square on both sides.

Divide each side by .

Square on both sides.

.

.

Substitute the values and in standard form.

.

The hyperbola equation is .

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