Ellipse
Equation of Ellipse
Grade 11
Question:
<p>The semi-minor axis is \(b = 2\) and the semi-major axis is \(a = 4\). Find the equation of the ellipse.</p>
<p>\(x^2 + 4y^2 = 16\)</p>
<p>\(4x^2 + y^2 = 16\)</p>
<p>\(x^2 + 4y^2 = 4\)</p>
<p>\(4x^2 + y^2 = 4\)</p>
Step-by-Step Solution
Key Concept: Use the standard form of ellipse equation with given semi-major axis a and semi-minor axis b: x²/a² + y²/b² = 1 when the major axis is along the x-axis.
<p><strong>Step 1:</strong> Identify given values: semi-major axis a = 4, semi-minor axis b = 2</p><p><strong>Step 2:</strong> Since a > b, the major axis is along the x-axis. Use standard form: x²/a² + y²/b² = 1</p><p><strong>Step 3:</strong> Substitute a = 4 and b = 2: x²/16 + y²/4 = 1</p><p><strong>Step 4:</strong> Verify: At x = 4, y = 0 (on major axis) ✓; At x = 0, y = 2 (on minor axis) ✓</p><p>∴ Answer: <strong>x²/16 + y²/4 = 1</strong></p>
Correct Answer: A