Question 593401: hello tutor, I need help with my question how do i find an equation of the ellipse having the given foci and sum of focal radii? thank you! :)
(0,0), (0,8);12
the sum of the focal radii 2a is 12 so a=7, the center between the foci is (0,0)right? this is all i can get up to, can you help me, thank you for your time!
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! hello tutor, I need help with my question how do i find an equation of the ellipse having the given foci and sum of focal radii? thank you! :)
(0,0), (0,8);12
**
Standard form of equation for an ellipse with vertical major axis: (x-h)^2/b^2+(y-k)^2/a^2=1, a>b, (h,k)=(x,y) coordinates of center.
..
For given ellipse
x-coordinate of center=0
y-coordinate of center=(8+0)/2=4 (midpoint formula)
center: (0,4)
Sum of focal radii=12=2a:
a=6
a^2=36
..
foci=8=2c
c=4
c^2=16
..
c^2=a^2-b^2
b^2=a^2-c^2=36-16=20
Equation:
x^2/20+(y-4)^2/36=1
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