Find the equation of an ellipse.

Question

Find the equation of an ellipse satisfying the given conditions. Foci: (-2,0) and (2,0); length of major axis: 10

Answer 1

Since the length of the major axis is 10,   the semi-major axis, a, is a = 5

The distance from the center to a focus is the c value, c = sqrt( a² - b²)  where b is the semi-minor axis.

 

 Since c =  2,    b = sqrt(21)

 

 The standard form is

 

     x² / a²  + y² /b²  = 1   So for this ellipse

 

   x² /25 + y²/21 = 1