Question
Download Solution PDFFind the equation of the directrix of the parabola x2 = 6y ?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFCONCEPT:
The following are the properties of a parabola of the form: x2 = 4ay where a > 0
- Focus is given by (0, a)
- Vertex is given by (0, 0)
- Equation of directrix is given by: y = - a
- Equation of axis is given by: x = 0
- Length of latus rectum is given by: 4a
- Equation of latus rectum is given by: y = a
CALCULATION:
Given: Equation of parabola is x2 = 6y
The given equation of parabola can be re-written as: x2 = 4 ⋅ (3/2)y----------(1)
Now by comparing the equation (1) with x2 = 4ay we get
⇒ a = 3/2
As we know that, the equation of directrix of the parabola of the form x2 = 4ay is given by: y = - a
So, the equation of directrix of the given parabola is: y = - 3/2
Hence, option C is the correct answer.
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