SOLUTION: Find the vertices and the foci of the ellipse with the given equation. Then draw the graph. 25x^2+16y^2=1

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Find the vertices and the foci of the ellipse with the given equation. Then draw the graph. 25x^2+16y^2=1      Log On


   

Question 960769: Find the vertices and the foci of the ellipse with the given equation. Then draw the graph. 25x^2+16y^2=1
Answer by lwsshak3(11628) About Me  (Show Source):
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Find the vertices and the foci of the ellipse with the given equation. Then draw the graph. 25x^2+16y^2=1
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given ellipse has a vertical major axis
Its standard form of equation: %28x-h%29%5E2%2Fb%5E2%2B%28y-k%29%5E2%2Fa%5E2%2B1
For given ellipse:
25%28x%5E2%29%2B16%28y%5E2%29=1
%28x%5E2%29%2F%281%2F25%29%2B%28y%5E2%29%2F%281%2F16%29=1
center: (0,0)
a^2=1/16
a=1/4
b^2=1/25
b=1/5
vertices: (0,±a)=(0, 0±(1/4))=(0, -(1/4)) and (0, (1/4)
c^2=a^2-b^2=1/16-1/25=25/400-16/400=9/400
c=3/20
foci: (0,±c)=(0, 0±(3/20))=(0, -(3/20)) and (0, (3/20)
..
y=.25(1-25x^2)^.5
see graph below: