Find the directrix of the parabola x^2 = -8y.
Answer and explanation
Correct answer: B. y = 2
- Step 1: Standard vertical parabola form: x^2 = 4py.
- Step 2: Set 4p = -8, giving p = -2.
- Step 3: Focus is at (0, p) = (0, -2).
- Step 4: Directrix is horizontal line opposite to focus: y = -p = -(-2) = 2.
Answer
y = 2.
Why not the others: 'y = -2' is the y-coordinate of the focus; 'x = 2' treats the parabola as horizontal; 'x = -2' gives directrix for a horizontal parabola opening left.
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