Question 933205: What does a graph of 18x^2+36y^2=648 look like? For a parabola, state the vertex, the focus, and the equation of the directrix. For a circle, state the center and radius. For an ellipse, state center, vertices, co-vertices, and foci. For a hyperbola, state the center, vertices, and foci.
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! What does a graph of 18x^2+36y^2=648 look like? For a parabola, state the vertex, the focus, and the equation of the directrix. For a circle, state the center and radius. For an ellipse, state center, vertices, co-vertices, and foci. For a hyperbola, state the center, vertices, and foci.
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18x^2+36y^2=648
divide both sides by 648
x^2/36+y^2/18=1
This is an equation of an ellipse with horizontal major axis.
Its standard form of equation:  , a>b, (h,k)=coordinates of center.
For given equation of an ellipse:
center: (0,0)
a^2=36
a=6
b^2=18
b=√18≈2.4
c^2=a^2-b^2=36-18=18
c=√18≈4.24
vertices: (0±a,0)=(0±6,0)=(-6,0) and (6,0)
foci:(0±c,0)=(0±2.4,0)=(-2.4,0) and (2.4,0)
co-vertices:=(0,0±c)=(0,0±2.4)=(0,-2.4) and (0,2.4)
see graph below:
y=(18(1-(x^2/36)))^.5
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