.
Rewrite the relation as a conic in standard form, then sketch the graph of the relation.
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2x = ====> square both sides ====>
= ====> collect all retms in the left side ====>
= 0 ====> Complete the square in the group of y-terms ====>
+ = 16 ====> Divide both sides by 16 ====>
+ = 1.
You got the standard equation of an ellipse.
The major axis is parallel to y-axis and is vertical.
The minor axis is parallel to x-axis and is horizontal.
The major semi-axis has the length of 4 units.
The minor semi-axis has the length of 2 units.
The ellipse is taller than wide.
The center is at the point (x,y) = (0,2).
The linear eccentricity is = = .
The foci are at the points (,) and (,)
Ellipse + = 1
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See the lessons in this site
- Ellipse definition, canonical equation, characteristic points and elements
- Standard equation of an ellipse
- Identify elements of an ellipse given by its standard equation
- Find the standard equation of an ellipse given by its elements
- General equation of an ellipse
- Transform a general equation of an ellipse to the standard form by completing the square
- Identify elements of an ellipse given by its general equation
Also, you have this free of charge online textbook in ALGEBRA-II in this site
ALGEBRA-II - YOUR ONLINE TEXTBOOK.
The referred lessons are the part of this online textbook under the topic
"Conic sections: Ellipses. Definition, major elements and properties. Solved problems".
Save the link to this textbook together with its description
Free of charge online textbook in ALGEBRA-II
https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson
into your archive and use when it is needed.