Identify the graph of the given nondegenerate conic sections: 3x^2 + 2y^2 + 12x - 4y + 2 = 0.

Identify the graph of the given nondegenerate conic sections: 3x^2 + 2y^2 + 12x - 4y + 2 = 0.

Question
Conic sections
asked 2021-02-25
Identify the graph of the given nondegenerate conic sections: \(3x^2 + 2y^2 + 12x - 4y + 2 = 0\).

Answers (1)

2021-02-26
Step 1 A nondegenerate conic section of the form, \(Ax^2 + By^2 + Cx + Dy + E=0\) Where A and B both are not zero. 1) A circle if \(A = B\) 2) A parabola if \(AB = 0\) 3) An ellipse if A is not equal to \(B and AB > 0\) 4) A hyperbola if \(AB < 0\) Step 2 Given that, \(3x^2 + 2y^2 + 12x − 4y + 2 = 0\) Here \(A = 3 and B = 2\) So A and B are not equal and \(AB = (3) (2) = 6 > 0\) Hence the graph of the equation is ellipse.
0

Relevant Questions

asked 2021-02-21
Identify the graph of the given nondegenerate conic sections: \(y^2 - 12x - 4y + 52 = 0\)
asked 2020-11-08
The type of conic sections for the nondegenerate equations given below. a) \(\displaystyle{8}{x}^{{{2}}}\ -\ {2}{y}^{{{2}}}\ -\ {3}{x}\ +\ {2}{y}\ -\ {6}={0}\) b) \(\displaystyle-{6}{y}^{{{2}}}\ +\ {4}{x}\ -\ {12}{y}\ -\ {24}={0}\) c) \(\displaystyle-{9}{x}^{{{2}}}\ -\ {4}{y}^{{{2}}}\ -\ {18}{x}\ +\ {12}{y}={0}\)
asked 2020-11-01
Identify the graph of the nondegenerate conic sections: \(4x^2 - 25y^2 - 24x + 250y - 489 = 0\).
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 2020-11-12
Find and calculate the center, foci, vertices, asymptotes, and radius, as appropriate, of the conic sections \(x^2 + 2y^2 - 2x - 4y = -1\)
asked 2021-01-25
Find the equation of the graph for each conic in standard form. Identify the conic, the center, the co-vertex, the focus (foci), major axis, minor axis, \(a^{2}, b^{2},\ and c^{2}.\) For hyperbola, find the asymptotes \(9x^{2}\ -\ 4y^{2}\ +\ 54x\ +\ 32y\ +\ 119 = 0\)
asked 2020-12-03
Instructions: Graph the conic section and make sure to label the coordinates in the graph. Include all the calculations needed to complete the graph. Give the standard form (SF) and the general form (GF) of the conic sections. HYPERBOLA: 1) The vertices are at (-2, 0) and (2, 0). The conjugate axis' length is 6.
asked 2020-11-22
Solve, a. If necessary, write the equation in one of the standard forms for a conic in polar coordinates \(r = \frac{6}{2 + sin \theta}\) b. Determine values for e and p. Use the value of e to identify the conic section. c. Graph the given polar equation.
asked 2020-10-18
Equations of Conic Sections Systems of Non-linear Equations Solve eeach problem systematically 1. Find all values of m so that the graph \(2mx^{2}\ -\ 16mx\ +\ my^{2}\ +\ 7y^{2} = 2m^{2}\ -\ 18m\) is a circle.
asked 2021-02-13
Whether the statement “I noticed that depending on the values for Aand B assuming that they are not both zero, the graph of \(Ax^2 + By^2 = C\) can represent any of the conic sections other than a parabola” “makes sense” or “does not make sense”, And explain your reasoning.
...