Q. 10 A5.0( 2 Votes )

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

x^{2} + 2y^{2} - 2x + 12y + 10 = 0

Answer :

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

⇒ x^{2} + 2y^{2} - 2x + 12y + 10 = 0

⇒ (x^{2} - 2x + 1) + 2(y^{2} + 6y + 9) - 9 = 0

⇒ (x - 1)^{2} + 2(y + 3)^{2} = 9

⇒

⇒

Comparing with the standard form

⇒ Centre = (p,q) = (1, - 3)

Here a^{2}>b^{2}

⇒ 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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