Engineering Board Exam Reviewer · Parabolas · medium

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

  1. x2 - 16 y = 0
  2. 16 x + y2 = 0
  3. x2 + 8 y = 0
  4. x2 + 16 y = 0

Answer

D. x2 + 16 y = 0

Solution

The axis is vertical and p=-4, so x2=4py=-16y, i.e. x2+16y=0.

More Parabolas questions

  1. Find the equation of the directrix of the parabola y2=-12x.
  2. Find the length of the latus rectum of the parabola x2=20y.
  3. Find the focus of the parabola y2=8x.
  4. Find the equation of the parabola with a vertical axis that passes through (0,0), (2,0) and (-1,3).
  5. Find the area bounded by the parabola y2=4x and its latus rectum.
  6. A parabolic reflector has a rim diameter of 20 cm and is 5 cm deep. How far from the vertex is the focus, in cm?
  7. Find the equation of the tangent line to the parabola y2=8x at the point (2,4).
  8. A point on the parabola y2=12x has an abscissa of 6. Find its distance from the vertex.
  9. Find the equation of the parabola with focus (2,3) and directrix x=-2.
  10. The point (4,4) lies on the parabola y2=4x. Find its distance from the focus.

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