Question
Download Solution PDFFind the equation of the parabola with vertex at (0, 0) and focus at (0, 4).
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
Parabola: The locus of a point which moves such that its distance from a fixed point is equal to its distance from a fixed straight line. (Eccentricity = e =1)
|
Equation |
x2 = 4ay |
|
Vertex |
(0, 0) |
|
Focus |
(0, a) |
|
Equation of the directrix |
y = -a |
|
Equation of the axis |
x = 0 |
|
Equation of Latus rectum |
y = a |
|
Length of Latus rectum |
4a |
Calculation:
Since the vertex is at (0, 0) and the focus is at (0, 4) which lies on the y-axis, the y-axis is the axis of the parabola.
Therefore, equation of the parabola is of the form x2 = 4ay.
x2 = 4 × 4y
∴ x2 = 16y.
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