write an equation of an ellipse whose center is at the origin given

Question

1. FOCI is at (± 3,0) and vertices at (±4,0)

2. FOCI is at (0,0±5) and length of major axis is 14

Answer 1

1.  The c value is 3 because of the foci's x coordinates, and the a value is 4. 
For an ellipse having major axis on the x-axis, as is the case here, the equation is x²/a² + y²/b² = 1 and the general relationship a^{2 -}- c² = b² is applicable.  This enables you to complete the job of obtaining the specific equation.

 

2.  For this ellipse, the major axis lies on the y =axis and so the position of the denominators (square of a and b) is reversed.  c = 5; a = 14.