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comentezq

Answered 2021-08-09
Author has **19928** answers

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 2021-08-08

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

a) \(\displaystyle{0.1}{x}^{{{2}}}+{0.6}{x}-{1.6}={0.2}{y}-{0.1}{y}^{{{2}}}\)

b) \(\displaystyle{2}{x}^{{{2}}}-{7}{x}{y}=-{y}^{{{2}}}+{4}{x}-{2}{y}-{1}\)

c) \(\displaystyle{8}{x}+{2}{y}={y}^{{{2}}}+{4}\)

a) \(\displaystyle{0.1}{x}^{{{2}}}+{0.6}{x}-{1.6}={0.2}{y}-{0.1}{y}^{{{2}}}\)

b) \(\displaystyle{2}{x}^{{{2}}}-{7}{x}{y}=-{y}^{{{2}}}+{4}{x}-{2}{y}-{1}\)

c) \(\displaystyle{8}{x}+{2}{y}={y}^{{{2}}}+{4}\)

asked 2021-08-08

Find the equations of the parabolas that share a vertex and a focus with the ellipse. Draw the conics. \(\displaystyle{25}{x}^{{2}}+{9}{y}^{{2}}={9}\)

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 2021-08-08

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 2021-08-12

Find the focus, equation of the directrices, lengths of major axis, minor axis and focal diameters, and draw the conic defined by \(\displaystyle{9}{x}^{{2}}+{16}{y}^{{2}}={1}\)