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What is the equation of the ellipse whose vertices are ( 5,0) and foci are at ( 4,0) ?

Options

  1. Ax^2 25 + y^2 9 =1
  2. Bx^2 16 + y^2 9 =1
  3. Cx^2 25 + y^2 16 =1
  4. Dx^2 9 + y^2 25 =1

Correct answer

A. x^2 25 + y^2 9 =1

Step-by-step solution

Given, vertices, (5,0) and (-5,0) foci (4,0) and (-4,0) i.e., a e =4 e = 4 a = 4 5 we know, b ^2= a ^2 (1- e ^2 ) aligned & =5^2 (1- ( 4 5 )^2 ) & =25 ( 25-16 25 )=9 & a ^2=25, ~b ^2=9 aligned Equation of ellipse is x^2 25 + y^2 9 =1

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