Question 473985
Consider the conic 2x^2+y^2=8. Answer the following without graphing:
Does it pass through the origin?why?
What is the maximum value of y?Justify.
For what values of x is y defined?Justify
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2x^2+y^2=8
divide by 8
x^2/4+y^2/8=1
This is an ellipse with vertical major axis and of the standard form: (x-h)^2/b^2+(y-k)^2/a^2=1
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Does it pass through the origin?
Given equation does not show h or k which means they are equal to zero which in turn means the center of the ellipse is at the origin. Curve itself does not pass thru origin.
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What is the maximum value of y?
a^2=8
a=√8
length of vertical major axis=2a=2√8
maximum value of y=top end point of vertical major axis=√8
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For what values of x is y defined?
b^2=4
b=2
length of minor axis=2b=4
Domain: [-2,2]