Identify and graph the conic whose equation is in attachment. \(\displaystyle{5}{x}^{{2}}+{4}{x}{y}+{2}{y}^{{2}}-{\frac{{{28}}}{{\sqrt{{5}}}}}{x}-{\frac{{{4}}}{{\sqrt{{5}}}}}{y}+{4}={0}\)

Identify each conic using eccentricity. (a) \(r=\frac{4}{1+3\sin \theta}\) (b) \(r=\frac{7}{1-3\cos \theta}\) (c) \(r=\frac{8}{6+5\cos \theta}\) (d) \(r=\frac{3}{2-3\sin \theta}\)

The front (and back) of a greenhouse have the same shape and dimensions shown below. The greenhouse is 40 feet long and the angle at the top of the roof is \(\displaystyle{90}^{{\circ}}\). Determine the volume of the greenhouse in cubic feet. Explain your solution.

Find the vertices and foci of the conic section. \(\frac{x^2}{4 }− \frac{y^2}{9} = 36\)