Ellipse
Equation of Ellipse
JEE Main 2020
Grade 11
Question:
If the co-ordinates of the two foci of an ellipse are $(\pm 3, 0)$ and the length of the minor axis is $8$, then the equation of the ellipse is:
(1) $\frac{x^2}{25} + \frac{y^2}{16} = 1$
(2) $\frac{x^2}{16} + \frac{y^2}{25} = 1$
(3) $\frac{x^2}{9} + \frac{y^2}{4} = 1$
(4) $\frac{x^2}{25} + \frac{y^2}{9} = 1$
Step-by-Step Solution
Key Concept: $c = 3$, $2b = 8 \Rightarrow b = 4$, $a^2 = b^2 + c^2 = 25$. Equation: $x^2/25 + y^2/16 = 1$.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (1)