Question 583310: endpoints of major axis at (-11,5) and (7,5), endpoints of minor axis at (-2,9) and(-2,1). Write an equation for the elipse that satisfies each set of conditions.
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! endpoints of major axis at (-11,5) and (7,5), endpoints of minor axis at (-2,9) and(-2,1). Write an equation for the elipse that satisfies each set of conditions.
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Standard form of equation for an ellipse with horizontal major axis:
(x-h)^2/a^2+(y-k)^2/b^2,a>b, (h,k) being the (x,y) coordinates of the center.
For given ellipse:
x-coordinate of center=(-11+7)/2=-4/2=-2 (use midpoint formula)
y-coordinate of center=(9+1)/2=10/2=5 (use midpoint formula)
center:(-2,5)
length of horizontal major axis=-11 to 7=18=2a
a=9
a^2=81
..
length of minor axis=9 to 1=8=2b
b=4
b^2=16
..
Equation of given ellipse:
(x+2)^2/81+(y-5)^2/16=1
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