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Equation of the ellipse whose axes are the axes of coordinates and which passes through the point (-3,1) and has eccentricity 2 5 is

Options

  1. A5 x^2+3 y^2-48=0
  2. B3 x^2+5 y^2-15=0
  3. C5 x^2+3 y^2-32=0
  4. D3 x^2+5 y^2-32=0

Correct answer

D. 3 x^2+5 y^2-32=0

Step-by-step solution

aligned & b ^2= a ^2 (1- e ^2 )= a ^2 (1- 2 5 )= a ^2 3 5 = 3 a ^2 5 & x ^2 a ^2 + y ^2 ~b ^2 =1 9 a ^2 + 5 3 a ^2 =1 & a ^2= 32 3 & ~b ^2= 32 5 aligned Required equation of ellipse 3 x^2+5 y^2-32=0

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