<p>Given equation is \(y^2 + 4y + 4x + 2 = 0\). The equation of the directrix of this parabola is:</p>
Step-by-Step Solution
Key Concept: Rewrite the equation in standard form (y - k)² = 4p(x - h) by completing the square, then identify the directrix as the vertical line x = h - p for a parabola opening horizontally.
<p><strong>Step 1:</strong> Complete the square for the y-terms in y² + 4y + 4x + 2 = 0</p><p>y² + 4y + 4 - 4 + 4x + 2 = 0</p><p>(y + 2)² + 4x - 2 = 0</p><p><strong>Step 2:</strong> Rearrange to standard form (y - k)² = 4p(x - h)</p><p>(y + 2)² = -4x + 2</p><p>(y + 2)² = -4(x - 1/2)</p><p><strong>Step 3:</strong> Identify parameters: vertex (h, k) = (1/2, -2) and 4p = -4, so p = -1</p><p><strong>Step 4:</strong> For a parabola (y - k)² = 4p(x - h) opening leftward (p < 0), the directrix is x = h - p</p><p>Directrix: x = 1/2 - (-1) = 1/2 + 1 = 3/2</p><p>∴ Answer: x = 3/2 (or equivalent form)</p>
Correct Answer: B