Question

121x²+64y²+242x+256y=7376Find the center, vertices, covertices, foci, Latus rectum

Answer 1

The given equation of the conic is:

`121x^2+64y^2+242x+256y=7376`

Solve as follows:

`\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 \\ ((x+1)^2)/((7753)/(121))+((y+2)^2)/((7753)/(64))=1 \end{gathered}`

Graph the ellipse as shown below:

The ellipse has center at (-1,-2)

Its vertices are:

`(-1,-2\pm\frac{\sqrt[]{7753}}{8})`

Covertices are:

`(-9.004647,2);(7.004647,2)`

Focii are:

`(-1,-2\pm\frac{\sqrt[]{441921}}{88})`

One of the latus rectum is:

`y=0.0032318937914x-9.5509884388909`