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Find the equation of the parabola with vertex at (0, 0) and focus at (0, 4).

  1. x2 = 2y
  2. x2 = 16y
  3. x2 = 4y
  4. x2 = 8y

Answer (Detailed Solution Below)

Option 2 : x2 = 16y
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Detailed Solution

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Concept:

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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