Question 559257: how would you solve and graph an ellipses with vertices:(4,3) and (4,9) and the focus at (4,8)?
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! how would you solve and graph an ellipses with vertices:(4,3) and (4,9) and the focus at (4,8)?
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Given data show this is an ellipse with a vertical major axis. Its equation of 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.
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For given ellipse:
center:(4,6)
length of vertical major axis=12=2a
a=6
a^2=36
c=4
c^2=16
..
c^2=a^2-b^2
b^2=a^2-c^2=36-16=20
b=√20≈4.47
..
Equation of given ellipse:
(x-4)^2/20+(y-6)^2/36=1
see graph below:
y=±(36-(36/20)(x-4)^2)^.5+6
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