Ellipse
Equation of Ellipse
Premium Question
Grade 11
Question:
The eccentricity of an ellipse with its centre at the origin is $1/2$. If one focus is at $(1, 0)$, then the equation of the ellipse is:
(1) $\frac{x^2}{4} + \frac{y^2}{3} = 1$
(2) $\frac{x^2}{3} + \frac{y^2}{4} = 1$
(3) $\frac{x^2}{16} + \frac{y^2}{12} = 1$
(4) $3x^2 + 4y^2 = 12$
Step-by-Step Solution
Key Concept: $e = 1/2$, focus $(1, 0) \Rightarrow c = 1$, $a = c/e = 2$, $b^2 = a^2 - c^2 = 3$. Equation: $x^2/4 + y^2/3 = 1$; equivalently $3x^2 + 4y^2 = 12$ (option 4 is the same).
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (1)