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The ellipse having its foci (0, 1) and major axis of length 5 is

Options

  1. A20 x^2+4 y^2=5
  2. B36 x^2+20 y^2=45
  3. C4 x^2+20 y^2=5
  4. D20 x^2+36 y^2=45

Correct answer

A. 20 x^2+4 y^2=5

Step-by-step solution

Since the foci of given ellipse lie on the Y -axis, it is vertical ellipse. Let the required equation be x^2 b^2 + y^2 a^2 =1 Where a^2>b^2 Foci are (0, c)=(0, 1) c=1a= length of the semi-major axis = 1 2 5 = 5 2 a^2= 5 4 Now, c^2=a^2-b^2 1= ( 5 2 )^2-b^2 b^2= 5 4 -1= 1 4 The required equation is x^2 1 / 4 + y^2 5 / 4 =1 4 x^2+ 4 y^2 5 =1 20 x^2+4 y^2=5

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