Engineering Board Exam Reviewer · Hyperbolas · hard

Find the distance between the foci of the hyperbola 9x2-16y2-36x-32y-124=0.

  1. 5
  2. 8
  3. 6
  4. 10

Answer

D. 10

Solution

Complete the squares: 9(x-2)2-16(y+1)2=144 (x-2)2/16-(y+1)2/9=1. c=sqrt(16+9)=5, so the foci are 2c=10 apart.

More Hyperbolas questions

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

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