Q5 of 76 Page 26

find the equation of the ellipse in the following cases:

eccentricity and major axis = 12

Given that we need to find the equation of the ellipse whose eccentricity is and the major axis is 12.


Let us assume the equation of the ellipse as (a2>b2).



We know that eccentricity(e) =


⇒


⇒


⇒


⇒


We know that length of ,ajor axis is 2a.


⇒ 2a = 12


⇒ a = 6


⇒ a2 = 36


⇒


⇒ b2 = 27


The equation of the ellipse is


⇒


⇒


⇒ 3x2 + 4y2 = 108


∴ The equation of the ellipse is 3x2 + 4y2 = 108.


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