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If the equation of parabola is 3y2 = 8x then which of the following statements is/are true: Equation of directrix is: 3x + 2 = 0 Equation of axis is: y = 0 Equation of latus rectum is: 3x - 2 = 0

If the equation of parabola is 3y2 = 8x then which of the following statements is/are true: Equation of directrix is: 3x + 2 = 0 Equation of axis is: y = 0 Equation of latus rectum is: 3x - 2 = 0 Correct Answer All (1), (2) and (3)

Concept:

For a parabola of the form y2 = 4ax where a > 0 we have:

  • Focus is given by: (a, 0)
  • Vertex is given by: (0, 0)
  • Equation of directrix is given by: x + a = 0
  • Equation of axis is given by: y = 0
  • Equation of latus rectum is given by: x - a = 0
  • Length of latus rectum is given by: 4a

Calculation:

Given: Equation of parabola is 3y2 = 8x

We can re-write the equation of given parabola as: y2 = 4 ⋅(2/3) ⋅ x

By comparing the above equation with y2 = 4ax where a > 0 we get: a = 2/3

So, equation of directrix is: 3x + 2 = 0.

Similarly, equation of axis is: y = 0 and equation of latus rectum is: 3x - 2 = 0.

Hence, option C is true.

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