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Question
If e is the eccentricity of the ellipse `x^2/a^2 + y^2/b^2` = 1 (a < b), then ______.
Options
b2 = a2(1 – e2)
a2 = b2(1 – e2)
a2 = b2(e2 – 1)
b2 = a2(e2 – 1)
Solution
If e is the eccentricity of the ellipse `x^2/a^2 + y^2/b^2` = 1 (a < b), then a2 = b2(1 – e2).
Explanation:
Given equation is `x^2/a^2 + y^2/b^2` = 1 (a < b)
∴ Eccentricity e = `sqrt(1 - a^2/b^2)`
⇒ `e^2 = 1 - a^2/b^2`
⇒ `a^2/b^2 = (1 - e)^2`
⇒ a2 = b2(1 – e2)
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