Engineering Board Exam Reviewer · Ellipses · hard

Find the distance between the foci of the ellipse 4x2+9y2-16x+18y-11=0.

  1. sqrt(5) 2.24
  2. 2 sqrt(5) 4.47
  3. 6
  4. 10

Answer

B. 2 sqrt(5) 4.47

Solution

Complete the squares: 4(x-2)2+9(y+1)2=36 (x-2)2/9+(y+1)2/4=1. c=sqrt(9-4)= 5, so the foci are 2c=2 5 4.47 apart.

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  1. Find the equation of the ellipse with center at the origin, vertices at ( 6,0) and a minor axis of length 8.
  2. A point on the ellipse 4x2+9y2=36 has x=2 and y>0. Find its y-coordinate.
  3. The major axis of an ellipse is twice its minor axis. Find the eccentricity.
  4. Find the area enclosed by the ellipse x2/16+y2/9=1.
  5. For any point on the ellipse 9x2+25y2=225, find the sum of its distances from the two foci.
  6. Find the foci of the ellipse (x-2)2/25+(y+1)2/9=1.
  7. Find the length of the latus rectum of the ellipse x2/36+y2/20=1.
  8. Find the equation of the ellipse with foci at ( 3,0) and a major axis of length 10.
  9. Find the eccentricity of the ellipse x2/25+y2/9=1.
  10. Find the foci of the ellipse x2/25+y2/9=1.

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