SOLUTION: 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

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: 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       Log On


   

Question 473985: Consider the conic 2x%5E2%2By%5E2=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.
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
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
**
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
..
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.
..
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
..
For what values of x is y defined?
b^2=4
b=2
length of minor axis=2b=4
Domain: [-2,2]