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Question
If the equation of the parabola is x2 = – 8y, find coordinates of the focus, the equation of the directrix and length of latus rectum.
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Solution
The given equation is of the form x2 = – 4ay where a is positive
Therefore, the focus is on y-axis in the negative direction and parabola opens downwards.
Comparing the given equation with standard form, we get a = 2.
Therefore, the coordinates of the focus are (0, –2)
And the the equation of directrix is y = 2
And the length of the latus rectum is 4a, i.e., 8.
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