Geo5.2.2

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Find the lengths of major axis,minor axis,latus rectum,eccentricity,centre,foci,equations of directrices of the ellipse {\frac  {x^{2}}{64}}+{\frac  {y^{2}}{36}}=1\,

Given ellipse is {\frac  {x^{2}}{64}}+{\frac  {y^{2}}{36}}=1\,

From the equation,

a^{2}=64,b^{2}=36\,

a=8,b=6,a>b\,

Major axis is 16 and Minor axis is 12.

Latus rectum is

{\frac  {2\cdot 36}{8}}=9\,

Length of the latusrectum is 9 units.

eccentricity e={\sqrt  {{\frac  {64-36}{64}}}}={\frac  {{\sqrt  {7}}}{4}}\,

Foci are (\pm 8\cdot {\frac  {{\sqrt  {7}}}{4}},0)=(\pm 2{\sqrt  {7}},0)\,

Equations of directrices are x=\pm {\frac  {32}{{\sqrt  {7}}}}\,

{\sqrt  {7}}x=\pm 32\,


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