Q. 10 B5.0( 2 Votes )

Find the ce

Answer :


Given that we need to find the centre, lengths of axes, eccentricity and foci of the ellipse x2 + 4y2 - 4x + 24y + 31 = 0.


x2 + 4y2 - 4x + 24y + 31 = 0


(x2 - 4x + 4) + 4(y2 + 6y + 9) - 9 = 0


(x - 2)2 + 4(y + 3)2 = 9




Comparing with the standard form


Centre = (p,q) = (2, - 3)


Here a2>b2


eccentricity(e) =






Length of the major axis 2a = 2(3) = 6


Length of the minor axis 2b = = 3


Foci = (p±ae,q)


Foci =


Foci =


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