What is the eccentricity of the ellipse given by (x^2 / 25) + (y^2 / 16) = 1?
Answer and explanation
Correct answer: B. 3/5
- Step 1: Identify major and minor semi-axes: a^2 = 25, so a = 5; b^2 = 16, so b = 4.
- Step 2: Compute focal distance c: c^2 = a^2 - b^2 = 25 - 16 = 9, so c = 3.
- Step 3: Calculate eccentricity: e = c / a = 3 / 5.
Answer
3/5.
Why not the others: '4/5' calculates b / a instead of c / a; '9/25' gives c^2 / a^2; '5/4' gives a / b which exceeds 1 (ellipses must have e < 1).
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