A conic section is said to be circle if the eccentricity e=1

Rivka Thorpe 2021-08-14 Answered
A conic section is said to be circle if the eccentricity e=1
image

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

firmablogF
Answered 2021-08-15 Author has 18596 answers
Explanation of conic section:
image
Not exactly what you’re looking for?
Ask My Question
47
 
Vasquez
Answered 2021-12-24 Author has 10020 answers

Step 1

The eccentricity of a conic section is a non-negative real number that uniquely characterizes its shape

Since the eccentricity of an ellipse \(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\);

\(a \geq b\) is given as

\(e=\sqrt{1-\frac{b^2}{a^2}}\)

A circle is an ellipse when a=b

so eccentricity of circle \(e=\sqrt{1-\frac{a^2}{a^2}}=\sqrt{1-1}=0\)

Answer: False

0

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Relevant Questions

asked 2021-08-12
Identify what type of conic section is given by the equation below and then find the center, foci, and vertices. If it is a hyperbola, you should also find the asymptotes.
\(\displaystyle{4}{x}^{{2}}-{24}{x}-{4}{y}+{28}={y}^{{2}}\)
asked 2021-08-07
Identify and sketch the graph of the conic section.
\(\displaystyle{9}{x}^{{2}}+{9}{y}^{{2}}+{18}{x}-{18}{y}+{14}={0}\)
asked 2021-08-09
Show that the equation represents a conic section. Sketch the conic section, and indicate all pertinent information (such as foci, directrix, asymptotes, and so on). \(\displaystyle{\left({a}\right)}{x}^{{2}}–{2}{x}–{4}{y}^{{2}}–{12}{y}=-{8}{\left({b}\right)}{2}{x}^{{2}}+{4}{x}-{5}{y}+{7}={0}{\left({c}\right)}{8}{a}^{{2}}+{8}{x}+{2}{y}^{{2}}–{20}{y}={12}\)
asked 2020-11-24

Decide if the equation defines an ellipse, a hyperbola, a parabola, or no conic section at all.
\(\displaystyle{\left({a}\right)}{4}{x}^{2}-{9}{y}^{2}={12}{\left({b}\right)}-{4}{x}+{9}{y}^{2}={0}\)
\(\displaystyle{\left({c}\right)}{4}{y}^{2}+{9}{x}^{2}={12}{\left({d}\right)}{4}{x}^{3}+{9}{y}^{3}={12}\)

asked 2020-12-28

For Exercise, an equation of a degenerate conic section is given. Complete the square and describe the graph of each equation.
\(\displaystyle{9}{x}^{2}+{4}{y}^{2}-{24}{y}+{36}={0}\)

asked 2021-08-10
Instructions:
Graph the conic section and make sure to label the coordinates in the graph. Give the standard form (SF) and the general form (GF) of the conic sections.
CIRCLES:
Center is at \(\displaystyle{\left({2},\ -{4}\right)}.\) the diameter's length is 6. The endpoints of the diameter is at \(\displaystyle{\left(-{1},\ -{4}\right)}\) and \(\displaystyle{\left({3},\ {6}\right)}.\)
asked 2021-08-10
Let A be a symmetric \(\displaystyle{2}\times{2}\) matrix and let k be a scalar. Prove that the graph of the quadratic equation \(\displaystyle{x}^{{T}}\) Ax=k is ,an ellipse, circle, or imaginary conic if \(\displaystyle{k}\ne{q}{0}\) and det A > 0
...