Question 558656: What is the equation of the ellipse with foci (0, 3), (0, -3) and co-vertices (1, 0), (-1, 0)?
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! What is the equation of the ellipse with foci (0, 3), (0, -3) and co-vertices (1, 0), (-1, 0)?
Given data shows this is an ellipse with vertical major axis of the standard form:
(x-h)^2/b^2+(y-k)^2/a^2=1, a>b, (h,k) being the (x,y) coordinates of the center.
..
For given ellipse:
center: (0,0)
c=3 (from foci)
c^2=9
b=1 (from co-vertices)
b^2=1
c^2=a^2-b^2
a^2=c^2+b^2=9+1=10
a=√10≈3.16
Equation of given ellipse:
x^2/1+y^2/10=1
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