Ellipse
Equation of Ellipse
JEE Main 2019
Grade 11
Question:
The equation of the ellipse, with axes as coordinate axes, passing through $(3, 1)$ with eccentricity $\sqrt{2/5}$, is:
(1) $3x^2 + 5y^2 = 32$
(2) $5x^2 + 3y^2 = 32$
(3) $3x^2 + 5y^2 = 15$
(4) $5x^2 + 3y^2 = 48$
Step-by-Step Solution
Key Concept: With major axis along $x$: $b^2 = a^2(1 - e^2) = 3a^2/5$. Substituting $(3, 1)$: $9/a^2 + 5/(3a^2) = 1 \Rightarrow a^2 = 32/3, b^2 = 32/5$. Equation: $3x^2 + 5y^2 = 32$.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (1)