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MHT CET202613 April 2026Evening ShiftMathematicsParabolaActual

The distance of the focus of the parabola y^2 = 16x from its directrix is...

Options

  1. A4
  2. B8
  3. C12
  4. D16

Correct answer

B. 8

Step-by-step solution

The given equation of the parabola is y^2 = 16x . Comparing this with the standard form y^2 = 4ax , we get 4a = 16 , which gives a = 4 . The coordinates of the focus are (a, 0) = (4, 0) . The equation of the directrix is x = -a , which is x = -4 . The distance between the focus and the directrix is the perpendicular distance from the point (4, 0) to the line x + 4 = 0 . Distance = |4 - (-4)| = 8 . Alternatively, the distance from the focus to the directrix for a parabola y^2 = 4ax is always 2a . Distance = 2 4 = 8

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