SOLUTION: What is the general conic form equation of the ellipse? Vertices: (6,9), (6,1) Foci: (6, 5+3.46101615) (6, 5-3.46101615)

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: What is the general conic form equation of the ellipse? Vertices: (6,9), (6,1) Foci: (6, 5+3.46101615) (6, 5-3.46101615)      Log On


   



Question 856828: What is the general conic form equation of the ellipse?
Vertices: (6,9), (6,1)
Foci: (6, 5+3.46101615) (6, 5-3.46101615)

Answer by lwsshak3(11628) About Me  (Show Source):
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What is the general conic form equation of the ellipse?
Ellipse has a vertical major axis.
Its standard form of equation: %28x-h%29%5E2%2Fb%5E2%2B%28y-k%29%5E2%2Fa%5E2=1, a>b, (h,k)=coordinates of center
Vertices: (6,9), (6,1)
Foci: (6, 5+3.46101615) (6, 5-3.46101615)
y-coordinate of center=5 (midpoint of 9 and 1)
x-coordinate of center=6
center: (6,5)
length of vertices=10=2a
a=5
a^2=25
foci:
c=3.46
c^2=11.98
c^2=a^2-b^2
b^2=a^2-c^2=25-11.98=13.03
Equation: %28x-6%29%5E2%2F13.03%2B%28y-5%29%5E2%2F25=1