Find the ecentricity, foci and the length of the latusrectum of the ellipse x²+4y²+8y–2x+1 = 0.
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Find eccentricity, foci & length of latus - rectum
of ellipse
∴x2+4y2+8y−2x+1=0
∴x2−2x+1+4y2+8y+2−1=0
(x−1)2+(2y+2)2−2=0
∴(x−1)2+(2y+2)2=2
∴2(x−1)2+(2)22(y+1)2=1
∴2(x−1)2+1/2(y+1)2=1
→x1=1 & y1=−1
Also,a=2 &b=21
centre =(1,
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