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Solution: Eccentricity-directrix approach Find an equation

Chapter 8, Problem 41RE

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QUESTION:

Eccentricity-directrix approach Find an equation of the following curves, assuming the center is at the origin. Graph the curve, labeling vertices, foci, asymptotes (if they exist), and directrices.

A hyperbola with vertices \((0, \pm 2)\) and directrices \(y=\pm 1\)

Questions & Answers

QUESTION:

Eccentricity-directrix approach Find an equation of the following curves, assuming the center is at the origin. Graph the curve, labeling vertices, foci, asymptotes (if they exist), and directrices.

A hyperbola with vertices \((0, \pm 2)\) and directrices \(y=\pm 1\)

ANSWER:

Solution 41RE

Step 1:

Given that

A hyperbola with vertices (0, ±2) and directrices y = ±1

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