Write the standard form equation for an ellipse with vertices at (2,5) and (2,-1), c=2?

From the information given, we know:





Center (2,2)


a=3


c=2


b^2=a^2-c^2


= 9-4


= 5


b=+-sq.root(5)





General form for Ellipse center at (h,k) is:





((x-h)^2/b^2)+((y-k)^2/a^2)=1





So answer is:


((x-2)^2/5)+((y-2)^2/9)=1

Write the standard form equation for an ellipse with vertices at (2,5) and (2,-1), c=2?
Standard form is (x-h)^2/b^2 + (y-k)^2/a^2 = 1


Apply the midpoint formula to the end point of the major axis to determine the center of the ellipse (h,k):


(h,k) = ([2+2]/2 , [5+(-1)]/2) = (2,2)


b = length of major axis/2 = [5+(-1)]/2 = 2


a = length of minor axis/2 = c/2 = 2/2 = 1, sooooo...


(x-2)^2/(2^2) + (y-2)^2/(1^2) = 1