The given equation of the conic is:
[tex]121x^2+64y^2+242x+256y=7376[/tex]Solve as follows:
[tex]\begin{gathered} 121x^2+242x+64y^2+256y-7376=0 \\ 121(x^2+2x+1)-121+64(y^2+4y+4)-256-7376=0 \\ 121(x+1)^2+64(y+2)^2=7753 \\ \frac{(x+1)^2}{\frac{7753}{121}}+\frac{(y+2)^2}{\frac{7753}{64}}=1 \end{gathered}[/tex]Graph the ellipse as shown below:
The ellipse has center at (-1,-2)
Its vertices are:
[tex](-1,-2\pm\frac{\sqrt[]{7753}}{8})[/tex]Covertices are:
[tex](-9.004647,2);(7.004647,2)[/tex]Focii are:
[tex](-1,-2\pm\frac{\sqrt[]{441921}}{88})[/tex]One of the latus rectum is:
[tex]y=0.0032318937914x-9.5509884388909[/tex]
