Q3 of 76 Page 26

Write the centre and eccentricity of the ellipse 3x2 + 4y2 – 6x + 8y – 5 = 0

Given that we need to find the centre and eccentricity of the ellipse 3x2 + 4y2 - 6x + 8y - 5 = 0.



⇒ 3x2 + 4y2 - 6x + 8y - 5 = 0


⇒ 3(x2 - 2x + 1) + 4(y2 + 2y + 1) = 12


⇒ 3(x - 1)2 + 4(y + 1)2 = 12


⇒


⇒


Comparing with the standard form


⇒ Centre = (p,q) = (1, - 1)


Here a2>b2


⇒ eccentricity(e) =


⇒


⇒


⇒


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