firmablogF

Answered 2021-08-15
Author has **18596** answers

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

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.

\(\displaystyle{4}{x}^{{2}}-{24}{x}-{4}{y}+{28}={y}^{{2}}\)

\(\displaystyle{4}{x}^{{2}}-{24}{x}-{4}{y}+{28}={y}^{{2}}\)

asked 2021-08-07

Identify and sketch the graph of the conic section.

\(\displaystyle{9}{x}^{{2}}+{9}{y}^{{2}}+{18}{x}-{18}{y}+{14}={0}\)

\(\displaystyle{9}{x}^{{2}}+{9}{y}^{{2}}+{18}{x}-{18}{y}+{14}={0}\)

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

\(\displaystyle{\left({a}\right)}{4}{x}^{2}-{9}{y}^{2}={12}{\left({b}\right)}-{4}{x}+{9}{y}^{2}={0}\)

\(\displaystyle{\left({c}\right)}{4}{y}^{2}+{9}{x}^{2}={12}{\left({d}\right)}{4}{x}^{3}+{9}{y}^{3}={12}\)

asked 2020-12-28

\(\displaystyle{9}{x}^{2}+{4}{y}^{2}-{24}{y}+{36}={0}\)

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 \(\displaystyle{\left({3},\ {6}\right)}.\)

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