The equation of the directrix of the parabola is
- A.
- B.
- C.
- D.
Show answer and solution
Correct option: D
Solution
Complete the square: y² + 4y + 4 = (y+2)², so the equation becomes (y+2)² = -4x - 2 + 4·1... let me redo:
y² + 4y + 4x + 2 = 0 → (y+2)² - 4 + 4x + 2 = 0 → (y+2)² = -4x + 2 = -4(x - 1/2).
This is a parabola of the form Y² = -4aX where Y = y+2, X = x - 1/2, and 4a = 4, so a = 1.
For Y² = -4aX, the directrix is X = a, i.e., x - 1/2 = 1, giving x = 3/2.
y² + 4y + 4x + 2 = 0 → (y+2)² - 4 + 4x + 2 = 0 → (y+2)² = -4x + 2 = -4(x - 1/2).
This is a parabola of the form Y² = -4aX where Y = y+2, X = x - 1/2, and 4a = 4, so a = 1.
For Y² = -4aX, the directrix is X = a, i.e., x - 1/2 = 1, giving x = 3/2.
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