Identify the conic with th e given equa­tion and give its equation in standard form 6x^2 - 4xy + 9y^2 - 20x - 10y - 5 = 0

melodykap 2020-11-09 Answered
Identify the conic with th e given equa­tion and give its equation in standard form \(6x^2 - 4xy + 9y^2 - 20x - 10y - 5 = 0\)

Expert Community at Your Service

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

Plainmath recommends

  • Ask your own question for free.
  • Get a detailed answer even on the hardest topics.
  • Ask an expert for a step-by-step guidance to learn to do it yourself.
Ask Question

Expert Answer

odgovoreh
Answered 2020-11-10 Author has 14684 answers
Given \(6x^2 - 4xy + 9y^2 - 20x - 10y - 5 = 0\) All degenerate conic sections have equations of the form \(Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0\).
\(Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0\) where A,B,C,D,E and F are constants. If \(B^2 − 4AC\) is less than zero, if a conic exists and A = C, it will be a circle If \(B^2 − 4AC\) is less than zero, if a conic exists , it will be ellipse. If \(B^2 − 4AC\) equals zero, if a conic exists, it will be a parabola. If \(B^2 − 4AC\) is greater than zero, if a conic exists, it will be a hyperbola. Here in equation \(6x^2 - 4xy + 9y^2 - 20x -10y - 5 = 0\), \(B^2 - 4 AC = 4^2 - 4 \cdot 6 \cdot 9\)
\(= 16 - 216\)
\(= - 200 < 0\) and \(A \neq C\) Hence it is an ellipse
Have a similar question?
Ask An Expert
23
 

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 2021-08-08
Find the equation by determining the type of the conic and draw its graph. \(\displaystyle{25}{x}^{{2}}+{9}{y}^{{2}}-{100}{x}+{54}{y}-{44}={0}\)
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 2020-10-18

The type of conic sections for the nondegenerate equations given below.

a) \(\displaystyle{6}{x}^{{{2}}}\ +\ {3}{x}\ +\ {10}{y}={10}{y}^{{{2}}}\ +\ {8}\)

b) \(\displaystyle{3}{x}^{{{2}}}\ +\ {18}{x}{y}={5}{x}\ +\ {2}{y}\ +\ {9}\)

c) \(\displaystyle{4}{x}^{{{2}}}\ +\ {8}{x}\ -\ {5}=\ -{y}^{{{2}}}\ +\ {6}{y}\ +\ {3}\)

asked 2021-08-07
Find the equation of the graph for each conic in standard form. Identify the conic, the center, the vertex, the co-vertex, the focus (foci), major axis, minor axis, \(\displaystyle{a}^{{2}},{b}^{{2}}\), and \(\displaystyle{c}^{{2}}\)?. For hyperbola, find the asymptotes. Sketch the graph. \(\displaystyle{9}{x}^{{2}}-{y}^{{2}}+{36}{x}+{4}{y}+{23}={0}\)
asked 2021-08-09
Find the equation of the graph for each conic in standard form. Identify the conic, the center, the vertex, the co-vertex, the focus (foci), major axis, minor axis, \(\displaystyle{a}^{{2}},{b}^{{2}}\), and \(\displaystyle{c}^{{2}}\)?. For hyperbola, find the asymptotes. Sketch the graph. \(\displaystyle{y}^{{2}}+{4}{y}-{2}{x}+{6}={0}\)
asked 2021-08-11
Find the equation of the graph for each conic in standard form. Identify the conic, the center, the vertex, the co-vertex, the focus (foci), major axis, minor axis, \(\displaystyle{a}^{{2}},{b}^{{2}}\), and \(\displaystyle{c}^{{2}}\)?. For hyperbola, find the asymptotes. Sketch the graph. \(\displaystyle{9}{x}^{{2}}+{25}{y}^{{2}}+{54}{x}-{50}{y}-{119}={0}\)
asked 2021-08-08
Find the equation of the graph for each conic in general form. Identify the conic, the center, the vertex, the co-vertex, the focus (foci), major axis, minor axis, \(\displaystyle{a}^{{2}}\), \(\displaystyle{b}^{{2}}\), and \(\displaystyle{c}^{{2}}\). For hyperbola,find the asymtotes.Sketch the graph
\(\displaystyle{9}{\left({y}-{3}\right)}^{{2}}-{4}{\left({x}+{5}\right)}^{{2}}={36}\)
...