/*! 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 71 Describe how to locate the foci ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 7: Problem 71

Describe how to locate the foci for \(\frac{x^{2}}{25}+\frac{y^{2}}{16}=1\)

Short Answer

Expert verified
The foci for the given equation \(\frac{x^{2}}{25}+\frac{y^{2}}{16}=1\) are located at (-3,0) and (3,0)

Step by step solution

01

Identify the Major and Minor Axes

Looking at the equation \(\frac{x^{2}}{25}+\frac{y^{2}}{16}=1\), we can see that the major axis 'a' is given by \(\sqrt{25} = 5\) and minor axis 'b' is given by \(\sqrt{16} = 4\). The larger denominator is the square of the major axis, and the smaller is the square of the minor axis.
02

Calculate the measure of the foci

Then use the formula \(c = \sqrt{a^2 - b^2}\) to calculate the distance from the center to a focus point. When we input the values for a and b, we got \(c = \sqrt{5^2 - 4^2} = \sqrt{9} = 3\)
03

Provide the foci coordinates

Finally, note that the foci will be located along the major axis, which in this case is along the x-axis. Here, the center of the ellipse is at the origin (0,0). So foci points will be 3 units left and right from the center. Consequently, the coordinates of the foci are (-3,0) and (3,0).

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

Will help you prepare for the material covered in the first section of the next chapter. Find the product of all positive integers from \(n\) down through 1 for \(n=5\).

Write an equation for the path of each of the following elliptical orbits. Then use a graphing utility to graph the two cllipses in the same viewing rectangle. Can you see why early astronomers had difficulty detecting that these orbits are ellipses rather than circles? \(\cdot\) Earth's orbit: Length of major axis: 186 million miles Length of minor axis: 185.8 million miles \(\cdot\) Mars's orbit: Length of major axis: 283.5 million miles Length of minor axis: 278.5 million miles

Find the vertex, focus, and directrix of each parabola with the given equation. Then graph the parabola. $$(x+2)^{2}=4(y+1)$$

Find the standard form of the equation of each parabola satisfying the given conditions. Focus: \((0,15) ;\) Directrix: \(y=-15\)

Wre a graphing utility to graph \(\frac{x^{2}}{4}-\frac{y^{2}}{9}=0 .\) Is the graph a hyperbola? In general, what is the graph of \(\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=0 ?\)
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Probability and Statistics

Read Explanation

Pure Maths

Read Explanation

Mechanics Maths

Read Explanation

Statistics

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.