Question 692119: Please help me figure out how to graph this ellipse:
(4/9)x^2 + 81y^2 = 1
I am unsure of what the fist step in this should be.
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! figure out how to graph this ellipse:
(4/9)x^2 + 81y^2 = 1
standard form of equation for an ellipse with horizontal major axis:
 , a>b, (h,k)=(x,y) coordinates of center.
...
standard form of equation for an ellipse with vertical major axis:
 , a>b, (h,k)=(x,y) coordinates of center.
note: a and b interchanged
...
To graph given ellipse:
The first step is to write the equation in standard form for an ellipse
(4/9)x^2 + 81y^2 =1
note the absence of h and k, so center is at (0,0)
a^2=9/4
b^2=1/81
a>b, so ellipse has a horizontal major axis
...
a^2=9/4
a=√(9/4)=3/2
vertices: (0±a,0)=(0±3/2,0)=(-3/2,0) and (3/2,0) (end points of horizontal major axis or x intercepts)
b^2=1/81
b=√(1/81)=1/9
co-vertices: (0,0±b)=(0,0±1/9)=(0,-1/9) and (0,1/9) (end points of minor axis or y intercepts)
..
you now have the center(0,0), vertices(-3/2,0) and (3/2,0) and co-vertices(0,-1/9) and (0,1/9)
with which you can draw the graph
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