What is the standard form of an ellipse and how do I find its eccentricity?
I have an equation x^2/25 + y^2/9 = 1 and I need to find eccentricity, foci, and length of major and minor axes. I always confuse which is a and which is b.
1 Answer
SDSiddharth Das
✓ Accepted
· 15d ago
▲ 16
Standard form: x^2/a^2 + y^2/b^2 = 1, where a > b (major axis along x-axis). From x^2/25 + y^2/9 = 1: a^2=25, b^2=9, so a=5, b=3. Semi-major axis = 5, semi-minor axis = 3. Major axis length = 2a = 10, minor axis length = 2b = 6. c^2 = a^2 - b^2 = 25 - 9 = 16, so c = 4. Foci: (+-4, 0). Eccentricity e = c/a = 4/5 = 0.8. Remember: for ellipse, 0 < e < 1. When a^2 is under x^2, major axis is horizontal. When a^2 is under y^2, major axis is vertical.
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