SOLUTION: Graph each equation. Identify the conic section and describe the graph and its line of symmetry. Then find the range and domain. {{{2x^2+y^2=36}}} Please explain step by step

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Question 972202: Graph each equation. Identify the conic section and describe the graph and its line of symmetry. Then find the range and domain.

Please explain step by step on how you got the answer. I really need help with conics!!
Found 2 solutions by josgarithmetic, stanbon:
Answer by josgarithmetic(39620) (Show Source):
You can put this solution on YOUR website!
You learn to derive each of the two-dimensional conic sections and to put them into a standard form. And then, you learn to recognize which conic section based on the form you see. This one is an ellipse.

Divide yours by 36.

Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
Graph each equation. Identify the conic section and describe the graph and its line of symmetry. Then find the range and domain.
2x^2+y^2=36}
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Please explain step by step on how you got the answer. I really need help with conics!!
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You have to recognize the standard forms for
the different conics.
General Form:: ax^2 + by^2 = 1
If a and b are equal and positive you have a circle
If a and b are unequal and positive you have an ellipse
If a and b have opposite signs you have a hyperbola
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Your Problem
Divide thru by 36 to get:
x^2/18 + y^2/36 = 1
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a and b are unequal and positive
You have an ellipse
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Domain... ?
y^2 = 36-2x^2
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y = +/-sqrt[36-2x^2]
Since 36-2x^2 must not be negative,
So, 2x^2 <= 36
x^2 <= 18
-3sqrt(2)<= x <=3sqrt(2)
That is the Domain
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Range... ?
2x^2 = 36-y^2
x^2 = 18-y^2/2
x = +-sqrt[18-y^2/2]
18-y^2/2 >= 0
y^2 <= 36
-6<= y <=6
That is the Range
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Cheers,
Stan H.
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