Find the coordinates of the foci for the ellipse:
(x + 3)^2 /9 + (y - 1)^2 /25 = 1
a. (3, -1) and (3, 5)
b. (-3, 3) and (-3, 1)
c. (-3, 5) and (-3, -3)
d. (1,1) and (-7,1)

Question

Find the coordinates of the foci for the ellipse:     
(x + 3)^2  /9  + (y - 1)^2   /25 = 1 
a. (3, -1) and (3, 5)  
b. (-3, 3) and (-3, 1)  
c. (-3, 5) and (-3, -3)             
d. (1,1) and (-7,1)

mertsj · Answer

c^2=a^2-b^2
c^2=25-9
c^2 = 16
c= 4,-4 
Note that the major axis of this ellipse is vertical since the big number is under y^2.  Also note that the center of this ellipse is (-3,1) and c = 4 so 4 units above (-3,1) is (-3,5).  That is one of the focal points.  The other one is 4 units below (-3,1) which is (-3,-3).  So 
(-3,5) and (-3,-3) or c