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Question

For the ellipse x2+4y2=9
 
  1. a focus is (33,0)
     
  2. a directrix is x=23
     
  3. the latus-rectum is 3/2
     
  4. the eccentricity is 1/2
     


Solution

The correct option is C the latus-rectum is 3/2
 
the latus-rectum is 3/2
x2+4y2=9
x29+y294=1
Here, a>b 
e=1a2b2
e=194
e=114
e=32
Latus rectum = 2b2a
2×94a=32
Focus= (±ae,0)
=(332,0)
Directrix x=±ae
=±332
=23

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