Find the vertex, foci, center, latus rectum, directrix of the equation
(x^2/64) +(y^2/55)=1
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The standard form of the equation of an ellipse centered at (h, k) with the major axis at the x-axis is given by
, where 
.
Comparing
and 
, we can see that h = 0 and k = 0. Therefore, the center of the ellipse is at the origin, (0, 0).
The coordinates of the vertices of an ellipse centered at (0, 0) and with the major axis in the x-axis is given by
. In this case, the vertices are at points 
and 
. That is, 
and 
.
The equations of the directrices of an ellipse centered at (0, 0) with the major axis in the x-axis is given by
, where 
is the eccentricity of the ellipse given by 
, where 
is the length of the foci obtained by 
. Here, 
. Thus, 
. Therefore, the equations of the directrices are 
.
The length of the latus rectum,
, of an ellipse centered at (0, 0) and with the major axis in the x-axis is given by 
.