Engineering Board Exam Reviewer · Ellipses · hard

Find the area of the largest rectangle that can be inscribed in the ellipse x2/25+y2/9=1.

  1. 15
  2. 60
  3. 30
  4. 45

Answer

C. 30

Solution

With vertex (5 ,3 ), the area is 4(5 )(3 )=30 2 , whose maximum is 30 (that is, 2ab).

More Ellipses questions

  1. Find the distance between the foci of the ellipse 4x2+9y2-16x+18y-11=0.
  2. Find the equation of the ellipse with center at the origin, vertices at ( 6,0) and a minor axis of length 8.
  3. A point on the ellipse 4x2+9y2=36 has x=2 and y>0. Find its y-coordinate.
  4. The major axis of an ellipse is twice its minor axis. Find the eccentricity.
  5. Find the area enclosed by the ellipse x2/16+y2/9=1.
  6. For any point on the ellipse 9x2+25y2=225, find the sum of its distances from the two foci.
  7. Find the foci of the ellipse (x-2)2/25+(y+1)2/9=1.
  8. Find the length of the latus rectum of the ellipse x2/36+y2/20=1.
  9. Find the equation of the ellipse with foci at ( 3,0) and a major axis of length 10.
  10. Find the eccentricity of the ellipse x2/25+y2/9=1.

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