Q. 10 C4.0( 3 Votes )

Find the centre, the lengths of the axes, eccentricity, foci of the following ellipse:

4x2 + y2 - 8x + 2y + 1 = 0

Answer :

Given that we need to find the centre, lengths of axes, eccentricity and foci of the ellipse 4x2 + y2 - 8x + 2y + 1 = 0.



4x2 + y2 - 8x + 2y + 1 = 0


4(x2 - 2x + 1) + (y2 + 2y + 1) - 4 = 0


4(x - 1)2 + (y + 1)2 = 4




Comparing with the standard form


Centre = (p,q) = (1, - 1)


Here b2>a2


eccentricity(e) =





Length of the major axis 2b = 2(2) = 4


Length of the minor axis 2a = 2(1) = 2


Foci = (p,q±be)


Foci =


Foci =


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