Question
If any point on an ellipse is (3 , 5 ), then what is the eccentricity of the ellipse?
NDA
Mathematics
Ellipse
2025
NDA 2025 (Phase 1)
NDA Mathematics Question (2025) — Solution
Options
- A. 4 3
- B. 4 5
- C. 3 4
- D. 1 2
Answer
B. 4 5
Step-by-step solution
Let x = 3 and y = 5 . x 3 = and y 5 = Squaring and adding both equations: x^2 9 + y^2 25 = ^2 + ^2 = 1 This represents an ellipse with a^2 = 9 and b^2 = 25. Since b > a, the eccentricity e is given by a^2 = b^2(1 - e^2). 9 = 25(1 - e^2) 1 - e^2 = 9 25 e^2 = 16 25 e = 4 5 Answer: 4 5
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