Chapter 11: Q. 166E (page 1134)

In the following exercises, graph.
$\frac{{(y + 3)}^{2}}{16} - \frac{{(x - 3)}^{2}}{36} = 1$

Short Answer

Expert verified

The graph is as below

Step by step solution

Step 1. Given information

The equation is $\frac{{(y + 3)}^{2}}{16} - \frac{{(x - 3)}^{2}}{36} = 1$

Draw the graph.

Step 2. Calculation

The y² term is positive, the transverse axis is vertical.

The hyperbola opens up and down.

Find the centre

Compare the equation with standard form $\frac{{(y - k)}^{2}}{a^{2}} - \frac{{(x - h)}^{2}}{b^{2}} = 1$

So, $(h, k) = (3, - 3)$ and $a^{2} = 16 \Rightarrow a = \pm 4$ , $b^{2} = 36 \Rightarrow b = \pm 6$

Sketch the rectangle that goes through the points 4 units above/below the centre 6 units left/right of centre.

Step 3. Draw the graph

Sketch the asymptotes and draw the graph.

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In the following exercises, graph.
$\frac{{(y + 3)}^{2}}{16} - \frac{{(x - 3)}^{2}}{36} = 1$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Calculation

Step 3. Draw the graph

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In the following exercises, graph.y+3216-x-3236=1

Short Answer

Step by step solution

Step 1. Given information

Step 2. Calculation

Step 3. Draw the graph

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Calculus

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Theoretical and Mathematical Physics

Decision Maths

Mechanics Maths

Study anywhere. Anytime. Across all devices.

In the following exercises, graph.
$\frac{{(y + 3)}^{2}}{16} - \frac{{(x - 3)}^{2}}{36} = 1$