Q5 of 76 Page 26

find the equation of the ellipse in the following cases:

Foci (± 3, 0), a = 4

Given that we need to find the equation of the ellipse whose foci are (±3,0) and a = 4.


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



⇒ a = 4


⇒ a2 = 16


We know that foci = (±ae,0)


⇒ ae = 3


⇒ 4e = 3


⇒


We know that eccentricity


⇒


⇒


⇒


⇒ b2 = 7


The equation of the ellipse is


⇒


⇒


⇒ 7x2 + 16y2 = 112


∴ The equation of the ellipse is 7x2 + 16y2 = 112.


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