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Question
If the focus of a parabola is (0, –3) and its directrix is y = 3, then its equation is ______.
Options
x2 = –12y
x2 = 12y
y2 = –12x
y2 = 12x
Solution
If the focus of a parabola is (0, –3) and its directrix is y = 3, then its equation is x2 = –12y.
Explanation:
According to the definition of parabola
`sqrt((x - 0)^2 + (y + 3)^2) = |(y - 3)/sqrt((0)^2 + (1)^2)|`
⇒ `sqrt(x^2 + y^2 + 9 + 6y) = |y - 3|`
Squaring both sides, we have
x2 + y2 + 9 + 6y = y2 + 9 – 6y
⇒ x2 + 9 + 6y = 9 – 6y
⇒ x2 = – 12y
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