Q17 of 76 Page 26

Find the equation of an ellipse whose vertices are (0, ± 10) and eccentricity.

Given that we need to find the equation of the ellipse whose vertices are (0,±10) and eccentricity .



Let us assume the equation of the ellipse as - - - - (1) (a2>b2).


We know that vertices of the ellipse are (0,±b)


⇒ b = 10


⇒ b2 = 100


We know that eccentricity


⇒


⇒


⇒


⇒


The equation of the ellipse is


⇒


⇒


⇒


⇒ 9x2 + 25y2 = 2500


∴ The equation of the ellipse is 9x2 + 25y2 = 2500.


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