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Question 1092965: Find the equation of ellipse with centre (1, 4),vertex at (1,7) and eccentricity e= 2/3. sketch the graph.
Answer by ikleyn(52903)   (Show Source):
You can put this solution on YOUR website! .
Notice that the center and the vertex lie in one vertical line x = 1.
Hence, the major axis is vertical line x = 1 parallel to y-axis.
Next, the major semi-axis length is the distance from the ellipse center to the vertex, i.e. 7-4 = 3 units.
Further, since the eccentricity is  , the minor semi-axis is  = 2 units, and the ellipse is taller than wide.
Thus the equation of the ellipse is
 } +  = 1.
Ellipse  +  = 1
See the lessons
- 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
in this site.
Also, you have this free of charge online textbook in ALGEBRA-II in this site
ALGEBRA-II - YOUR ONLINE TEXTBOOK.
The referred lesson is 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.
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