Chapter 11: Q. 165E (page 1134)

In the following exercises, graph.
$\frac{{(y - 4)}^{2}}{16} - \frac{{(x + 1)}^{2}}{25} = 1$

Short Answer

Expert verified

The graph is as below

Step by step solution

Step 1. Given information

The equation is $\frac{{(y - 4)}^{2}}{16} - \frac{{(x + 1)}^{2}}{25} = 1$

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, $(h, k) = (- 1, 4)$ and $a^{2} = 16 \Rightarrow a = \pm 4$

$b^{2} = 25 \Rightarrow b = \pm 5$

Sketch the rectangle that goes through the points 4 units above/below the centre

5 units left/right of centre

Step 3. Draw the graph

Sketch the graph using asymptotes.

The graph is

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

In the following exercises, graph.
$\frac{{(y - 4)}^{2}}{16} - \frac{{(x + 1)}^{2}}{25} = 1$

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

Theoretical and Mathematical Physics

Calculus

Mechanics Maths

Logic and Functions

Probability and Statistics

Applied Mathematics

Study anywhere. Anytime. Across all devices.

In the following exercises, graph.y-4216-x+1225=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

Theoretical and Mathematical Physics

Calculus

Mechanics Maths

Logic and Functions

Probability and Statistics

Applied Mathematics

Study anywhere. Anytime. Across all devices.

In the following exercises, graph.
$\frac{{(y - 4)}^{2}}{16} - \frac{{(x + 1)}^{2}}{25} = 1$