Engineering Board Exam Reviewer · Ellipses · medium

Find the equation of the ellipse with foci at ( 3,0) and a major axis of length 10.

  1. x216 + y225 = 1
  2. x225 + y216 = 1
  3. x225 + y29 = 1
  4. x225 - y216 = 1

Answer

B. x225 + y216 = 1

Solution

2a=10 a=5 and c=3, so b2=a2-c2=16. The equation is x2/25+y2/16=1.

More Ellipses questions

  1. Find the eccentricity of the ellipse x2/25+y2/9=1.
  2. Find the foci of the ellipse x2/25+y2/9=1.
  3. Find the length of the major axis of the ellipse x2/25+y2/9=1.
  4. Find the distance from the center of the ellipse x2/25+y2/9=1 to each directrix.
  5. Find the area of the largest rectangle that can be inscribed in the ellipse x2/25+y2/9=1.
  6. Find the distance between the foci of the ellipse 4x2+9y2-16x+18y-11=0.
  7. Find the equation of the ellipse with center at the origin, vertices at ( 6,0) and a minor axis of length 8.
  8. A point on the ellipse 4x2+9y2=36 has x=2 and y>0. Find its y-coordinate.
  9. The major axis of an ellipse is twice its minor axis. Find the eccentricity.
  10. Find the area enclosed by the ellipse x2/16+y2/9=1.

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