/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 46 Determine the equation in standa... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 9: Problem 46

Determine the equation in standard form of the ellipse centered at the origin that satisfies the given conditions. Minor axis of length \(6 ;\) major axis of length \(14 ;\) major axis horizontal

Short Answer

Expert verified
The equation of the ellipse is \((\frac{x^2}{49}) + (\frac{y^2}{9}) = 1\).

Step by step solution

01

Determine Half Lengths

First, it should be noted that a and b in the ellipse equation represent half the major and minor axis lengths. As such, half the major axis length is \(\frac{14}{2} = 7\), and half the minor axis length is \(\frac{6}{2} = 3\).
02

Identify Major Axis

The major axis is shifted along the horizontal axis (that is, along the x-axis). Therefore, a bigger denominator should be under the x-term in the ellipse equation. This makes the ellipse equation to be \((\frac{x^2}{7^2}) + (\frac{y^2}{3^2}) = 1\).
03

Simplify Equation

Upon simplification, the expression turns out to be \((\frac{x^2}{49}) + (\frac{y^2}{9}) = 1\), which is the equation of the ellipse in standard form.

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.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

This set of exercises will draw on the ideas presented in this section and your general math background. Write the equation for the set of points whose distances from the points (3,2) and (3,-8) differ by 6

Suppose Jacob hits a baseball from a tee that is 3 feet tall. He hits the ball with an initial velocity of 120 feet per second at an angle of \(50^{\circ}\) to the horizontal. What is the maximum distance the ball will travel?

Determine the equation in standard form of the hyperbola that satisfies the given conditions. Transverse axis of length \(6 ;\) one vertex at (7,8)\(;\) one focus at (7,5)

Explain why there is a difference between the graphs of the following sets (a) and (b). (a) \(x=t, y=t+1,0 \leq t \leq 1\) (b) \(x=-t, y=-t+1,0 \leq t \leq 1\)

Identify and graph the conic section given by each of the equations. $$r=\frac{4}{1+2 \cos \theta}$$
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Discrete Mathematics

Read Explanation

Statistics

Read Explanation

Probability and Statistics

Read Explanation

Mechanics Maths

Read Explanation

Geometry

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.