Find an equation for the ellipse

Question

Find an equation for the ellipse that satisfies the given conditions:

 

Foci (1, ±4)

 

Vertices (1, ±7)

Answer 1

One can tell by plotting the foci and vertices, that the ellipse will be vertical. The plotted points will also show the center is (1,0).

(x-h)² + (y-k)² = 1      (h,k) = (1,0) 

   b²          a²

2a = 14,the length of the major axis.    a = 7

c = the distance between the focus and the center, c = 4

c² = a² - b²

16 = 49 - b² 

b² = 33

(x-1)² +  y² = 1  33        49