Question

# Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse. 36x2+4y2=144

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Solution

## The equation of given ellipse is, 36x2+4y2=144 i.e.36x214+4y2144=1⇒x24+y236=1.Now 36>4⇒a2=36 and b2=4So the equation of ellipse in standard form isy2a2+x2b2=1 ∴a2=36⇒a=6 and b2=4⇒b=2We know that c=√a2−b2∴c=√36−4=√32=4√2∴Coordinates of foci are (0,+c)i.e.(0,±√2)Coordinates of vertices are (0,±a)i.e.(0,±6)Length of major axis=2a=2×6=12Length of minor axis=2b=2×2=4Eccentricity(e)=ca=4√26=2√23Length of latus rectum=2b2a=2×46=43

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