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NDA2023MathematicsEllipseActual

Paragraph: Consider the following for the next two (02) items that follow: P (x, y) is any point on the ellipse x^2+4 y^2=1 . Let E, F be the foci of the ellipse. Question: Consider the following points: 1. ( 3 2 , 0 ) 2. ( 3 2 , 1 4 ) 3. ( 3 2 ,- 1 4 ) Which of the following points lie on latus rectum of ellipse?

Options

  1. A1 and 2 only
  2. B2 and 3 only
  3. C1 and 3 only
  4. D1,2 and 3

Correct answer

D. 1,2 and 3

Step-by-step solution

b^2=a^2 (1-e^2 ) 1 4 =1-e^2 e= 3 2 focii ( a e, 0)= ( 3 2 , 0 ) Equation of latus rectum, x= 3 2 All 3 points lie on latus rectum

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