Find the eccentricity, foci,vertices and the length of the latus rectum of the ellipse x2+4y2+8y-2x+1=0
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We have been given the equation of ellipse as:
Let us try to write the equation of ellipse in the standard notation:
Shifting the origin to (1,-1) without rotating the axes. We get the new coordinates of the ellipse:
Our new equation of the ellipse is:
It is in the form of :
where,
On comparison with the older equation we get:
and
1. Finding the eccentricity of the ellipse:
Plugging the values of 'a' and 'b', we get:
Therefore, the eccentricity of the ellipse is .
Coordinates of focii are:
Coordinates of the focii with respect to the old axes is:
(since we had shifted the origin to (1, -1))
Length of Latus rectum is given by:
.
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