Chapter 11: Q. 11.54 (page 1126)

Graph $\frac{x^{2}}{9} - \frac{y^{2}}{16} = 1$

Short Answer

Expert verified

The plotted graph of $\frac{x^{2}}{9} - \frac{y^{2}}{16} = 1$ is given below

Step by step solution

Step 1. Given information

Given that the equation of the hyperbola $\frac{x^{2}}{9} - \frac{y^{2}}{16} = 1$ .

We need to plot the graph of the given hyperbola.

Step 2. Calculations for graphing hyperbola

The standard form of hyperbola is $\frac{x^{2}}{9} - \frac{y^{2}}{16} = 1$ . Since term x² is positive transverse axis is on X-axis and horizontal. Here $a^{2} = 9 s o a = \pm 3$ , then the vertices $(- 3, 0) a n d (3, 0)$ are on x -axis. Since $a = \pm 3$ , the rectangle intersects at x-axis and role="math" localid="1645570371884" $b = \pm 4$ the rectangle intersect at y axis at the points $(0, - 4) a n d (0, 4)$ . Asymptotes of the given hyperbola is $y = \frac{4}{3} x a n d y = - \frac{4}{3} y$ .

Step. 4 Sketching the Graph of hyperbola

The sketched graph of hyperbola using the given information is given below

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Graph $\frac{x^{2}}{9} - \frac{y^{2}}{16} = 1$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Calculations for graphing hyperbola

Step. 4 Sketching the Graph of hyperbola

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Graphx29-y216=1

Short Answer

Step by step solution

Step 1. Given information

Step 2. Calculations for graphing hyperbola

Step. 4 Sketching the Graph of hyperbola

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

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Study anywhere. Anytime. Across all devices.

Graph $\frac{x^{2}}{9} - \frac{y^{2}}{16} = 1$