The eccentricity e gives us the size of an ellipse

Asked by admin @ 22/11/2021 in Mathematics viewed by 284 People

The eccentricity e of an ellipse is defined as the number c/a, where a is the distance of a vertex from the center and c is the distance of a focus from the center. Because a>c, it follows that e<1. Write a brief paragraph about the general shape of each of the following ellipses. Be sure to justify your conclusions. (a) Eccentricity close to 0 (b) Eccentricity=5 (c) Eccentricity close to 1

Answered by admin @ 22/11/2021

Answer:

Check below, please.

Step-by-step explanation:

Hi, there!

Since we can describe eccentricity as $e=\frac{c}{a}$

a) Eccentricity close to 0

An ellipsis with eccentricity whose value is 0, is in fact, a degenerate one almost a circle. An ellipse whose value is close to zero is almost a degenerate circle. The closer the eccentricity comes to zero, the more rounded gets the ellipse just like a circle. (Check picture, please)

$\frac{x^2}{a^2} +\frac{y^2}{b^2} =1 \:(Ellipse \:formula)\\a^2=b^2+c^2 \: (Pythagorean\: Theorem)\:a=longer \:axis.\:b=shorter \:axis)\\a^2=b^2+(0)^2 \:(c\:is \:the\: distance \: the\: Foci)\\\\a^2=b^2 \\a=b\: (the \:halves \:of \:each\:axes \:measure \:the \:same)$

b) Eccentricity =5

$5=\frac{c}{a} \:c=5a$

An eccentricity equal to 5 implies that the distance between the Foci has to be five (5) times larger than the half of its longer axis! In this case, there can't be an ellipse since the eccentricity must be between 0 and 1 in other words:

$If\:e=\frac{c}{a} \:then\:c>0 , and\: c>0 \:then \:1>e>0$

c) Eccentricity close to 1

In this case, the eccentricity close or equal to 1 We must conceive an ellipse whose measure for the half of the longer axis a and the distance between the Foci 'c' they both have the same size.

$a=c\\\\a^2=b^2+c^2\:(In \:the\:Pythagorean\:Theorem\: we \:should\:conceive \:b=0)$

$Then:\\\\a=c\\e=\frac{c}{a}\therefore e=1$

Match the logical fallacy to the correct definition. match term definition ----incorrectly assumes that one event causes another a) fear claims that one -------action leads to a series of undesirable events b) false dichotomy claims ---------something is true because most people agree c) slippery slope appeals to ------the desire to be safe d) popularity gives two choices, one of which is not -------truly an option e) post hoc

Asked by maham237 @ 13/01/2021 in English viewed by 533 persons

Take any three non-collinear points a b c and draw triangle a,b,c. through each vertex of the triangle draw a line parallel to the opposite side using ruler and compass

Asked by wiki @ 15/11/2022 in Mathematics viewed by 1561 persons

The eccentricity e gives us the size of an ellipse

Similar Questions

Did the louisiana purchase doubled the size of the us

Which animal gives us wool

What is the largest state in the us by size

We should be content with what life gives us

Advanced technology gives us conclusive evidence of past events

What gives the us government the power to collect taxes

Overcoming fixed mindset: a step-by-step guide to cultivating a growth mindset

Which of the following would best complete this list?

What had the king decided to do before he saw the spider

Describe the karez in your own words

What is 8 + (x + 5)?

Take any three non-collinear points a b c and draw triangle a,b,c. through each vertex of the triangle draw a line parallel to the opposite side using ruler and compass

What is the topic of the info grapher

Elephant kills 11 in nepal , woman rescued from a friendly dolphine

Most viewed questions in Mathematics

Unit 6 similar triangles homework 2 similar figures answer key

All things algebra unit 7 polygons and quadrilaterals answer key

Gina wilson all things algebra 2016 answer key unit 11

Unit 1 geometry basics homework 4 angle addition postulate answers

Unit 6 exponents and exponential functions homework 8 answer key

The manager of a vacation resort believes that the ages

What is 271 403 rounded to the nearest ten thousand

Unit 1 geometry basics homework 3 angle relationships answer key

Homework 2 parallelograms

Why would a prism beat a sphere in a competition?

John wants to send a letter to peter

An artist sells a painting for 20.50 but uses 5.75

Unit 4 congruent triangles homework 1 classifying triangles answer key

Unit 4 congruent triangles homework 2 angles of triangles

Compare the values of the 2s and 5s in 55220