Chapter 10: Q. 9 (page 667)

Answer Problems 9–11 using the figure.
The equation of the hyperbola is of the form
(a) $\frac{{(x - h)}^{2}}{a^{2}} - \frac{{(y - k)}^{2}}{b^{2}} = 1$
(b) $\frac{{(y - h)}^{2}}{a^{2}} - \frac{{(x - k)}^{2}}{b^{2}} = 1$

Short Answer

Expert verified

The equation of the hyperbola is of the form $\frac{{(y - h)}^{2}}{a^{2}} - \frac{{(x - k)}^{2}}{b^{2}} = 1$ since the graph of the hyperbola opens up and down.

Step by step solution

Step 1. Given Information

The graph of the hyperbola is:

We need to find if the hyperbola is of the form $\frac{{(x - h)}^{2}}{a^{2}} - \frac{{(y - k)}^{2}}{b^{2}} = 1$ or $\frac{{(y - h)}^{2}}{a^{2}} - \frac{{(x - k)}^{2}}{b^{2}} = 1$

Step 2. Concept

If the equation of the hyperbola is of the form $\frac{{(y - k)}^{2}}{a^{2}} - \frac{{(x - h)}^{2}}{b^{2}} = 1$ , then the graph of the hyperbola opens up and down.

If the equation of the hyperbola is of the form $\frac{{(x - h)}^{2}}{a^{2}} + \frac{{(y - k)}^{2}}{b^{2}} = 1$ then the graph of the hyperbola opens towards the left and right.

Step 3. Explanation

Since the graph of the hyperbola opens up and down, the equation of the hyperbola is of the form $\frac{{(y - h)}^{2}}{a^{2}} - \frac{{(x - k)}^{2}}{b^{2}} = 1$ .

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Answer Problems 9–11 using the figure.
The equation of the hyperbola is of the form
(a) $\frac{{(x - h)}^{2}}{a^{2}} - \frac{{(y - k)}^{2}}{b^{2}} = 1$
(b) $\frac{{(y - h)}^{2}}{a^{2}} - \frac{{(x - k)}^{2}}{b^{2}} = 1$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Concept

Step 3. Explanation

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Answer Problems 9–11 using the figure.The equation of the hyperbola is of the form(a) (x-h)2a2-(y-k)2b2=1(b)(y-h)2a2-(x-k)2b2=1

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Concept

Step 3. Explanation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Applied Mathematics

Calculus

Logic and Functions

Pure Maths

Statistics

Study anywhere. Anytime. Across all devices.

Answer Problems 9–11 using the figure.
The equation of the hyperbola is of the form
(a) $\frac{{(x - h)}^{2}}{a^{2}} - \frac{{(y - k)}^{2}}{b^{2}} = 1$
(b) $\frac{{(y - h)}^{2}}{a^{2}} - \frac{{(x - k)}^{2}}{b^{2}} = 1$