Chapter 11: Q. 11.53 (page 1126)

Graph $\frac{x^{2}}{16} - \frac{y^{2}}{4} = 1$

Short Answer

Expert verified

The plotted graph of $\frac{x^{2}}{16} - \frac{y^{2}}{4} = 1$ is given below

Step by step solution

Step 1. Given information

Here equation of the hyperbola is given.

we have to plot the graph of the given hyperbola.

Step .2 Calculations for plotting hyperbola

The equation in standard form is $\frac{x^{2}}{16} - \frac{y^{2}}{4} = 1$ . Here x² is positive hence transverse axis is on x-axis and horizontal. Since $a^{2} = 16 t h e n a \pm 4 .$ The vertices $(- 4, 0) a n d (4, 0)$ are on the x-axis .Since $a = \pm 4,$ the rectangle intersects at x-axis at the vertices and $b = \pm 2$ ,he rectangle intersects at y-axis at $(0, 2) a n d (0, - 2)$ . Asymptotes are $y = \frac{2}{4} x a n d y = - \frac{2}{4} x$ .

Step.3 Graph of hyperbola

The graph of the hyperbola $\frac{x^{2}}{16} - \frac{y^{2}}{4} = 1$ is given below

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Graph $\frac{x^{2}}{16} - \frac{y^{2}}{4} = 1$

Short Answer

Step by step solution

Step 1. Given information

Step .2 Calculations for plotting hyperbola

Step.3 Graph of hyperbola

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Graphx216-y24=1

Short Answer

Step by step solution

Step 1. Given information

Step .2 Calculations for plotting hyperbola

Step.3 Graph of hyperbola

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

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Geometry

Study anywhere. Anytime. Across all devices.

Graph $\frac{x^{2}}{16} - \frac{y^{2}}{4} = 1$