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Question
Given the ellipse with equation 9x2 + 25y2 = 225, find the eccentricity and foci.
Solution
Given equation of ellipse is 9x2 + 25y2 = 225
⇒ `9/225 x^2 + 25/225 y^2` = 1
⇒ `x^2/25 + y^2/9` = 1
Here a = 5 and b = 3
b2 = a2(1 – e2)
⇒ 9 = 25(1 – e2
⇒ 1 – e2 = `9/25`
⇒ e2 = `1 - 9/25 = 16/25`
e = `4/5`
Now foci = (± ae, 0)
= `(+- 5 xx 4/5, 0)`
= (± 4, 0).
Hence, eccentricity = `4/5`, foci = (± 4, 0).
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