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4th Edition

James Stewart

Publisher: Cengage Learning

ISBN: 9781337687805

Chapter B, Problem 52E

**(a)**

To determine

**To calculate: **To find the foci and asymptotes of the hyperbola

Expert Solution

Foci of hyperbola are

Asymptotes of hyperbola are

**Given information: **Equation of hyperbola is

**Formula Used:**

Standard equation of hyperbola is

where

Foci of above hyperbola is

Asymptotes of

**Calculation:**

Equation of ellipse is given as

Rewrite the equation as follows:

On comparing the equation with standard equation of hyperbola,

Value of

Thus, foci of hyperbola are

Now, asymptotes of hyperbola are calculated as

On sketching the hyperbola:

**Conclusion:**

Hence, foci of hyperbola are

**(b)**

To determine

**To calculate: **To sketch the graphof the hyperbola

Expert Solution

The graph of hyperbola is sketched

**Given information: **Equation of hyperbola is

**Formula Used:**

Standard equation of hyperbola is

where

Foci of above hyperbola is

Asymptotes of

**Calculation:**

Equation of ellipse is given as

Foci and asymptotes are found out by reversing the roles of

Thus, foci are

Using the values of equation

Thus, foci of hyperbola are

Now, asymptotes of hyperbola are calculated as

On sketching the hyperbola:

**Conclusion:**

Hence, graph of hyperbola is sketched