Q10 of 76 Page 26

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

x2 + 2y2 - 2x + 12y + 10 = 0

Given that we need to find the centre, lengths of axes, eccentricity and foci of the ellipse x2 + 2y2 - 2x + 12y + 10 = 0.



⇒ x2 + 2y2 - 2x + 12y + 10 = 0


⇒ (x2 - 2x + 1) + 2(y2 + 6y + 9) - 9 = 0


⇒ (x - 1)2 + 2(y + 3)2 = 9


⇒


⇒


Comparing with the standard form


⇒ Centre = (p,q) = (1, - 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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