Hyperbolas — Engineering Board Exam Practice Questions

12 free engineering board exam reviewer questions on Hyperbolas (Analytic Geometry), each with the correct answer and a worked solution.

  1. Find the distance between the foci of the hyperbola 9x2-16y2-36x-32y-124=0.
  2. Find the distance between the two directrices of the hyperbola x2/16-y2/9=1.
  3. The point P lies on the rectangular hyperbola xy=18 and has x=3. Find its distance from the origin.
  4. For any point on the hyperbola x2/25-y2/144=1, find the absolute difference of its distances from the two foci.
  5. Find the vertices of the hyperbola (x-1)2/9-(y+2)2/4=1.
  6. Find the equation of the hyperbola with vertices at (0, 4) and asymptotes y= 2x.
  7. Find the length of the latus rectum of the hyperbola x2/9-y2/16=1.
  8. Find the equation of the hyperbola with foci at ( 5,0) and a transverse axis of length 6.
  9. Find the eccentricity of the hyperbola x2/16-y2/9=1.
  10. Find the equations of the asymptotes of the hyperbola x2/16-y2/9=1.
  11. Find the foci of the hyperbola x2/16-y2/9=1.
  12. Find the length of the transverse axis of the hyperbola x2/16-y2/9=1.