Question:
If the focus of a parabola is \( (0, -3) \) and its directrix is \( y = 3 \), then its equation is:
If the focus of a parabola is \( (0, -3) \) and its directrix is \( y = 3 \), then its equation is:
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For a parabola, the equation depends on the orientation and focal distance \( a \), calculated from the focus and directrix.
Updated On: Mar 10, 2025
- \( x^2 = 12y \)
- \( x^2 = -12y \)
- \( y^2 = 12x \)
- \( y^2 = -12x \)
- \( y^2 = x \)
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The Correct Option is B
Solution and Explanation
The vertex of the parabola is the midpoint of the focus and directrix:
\[
\left( 0, \frac{-3 + 3}{2} \right) = (0,0)
\]
The standard form of a parabola with its vertex at \( (0,0) \) and vertical axis is:
\[
x^2 = 4ay
\]
The focal distance is:
\[
a = -3
\]
Thus,
\[
x^2 = -12y
\]
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