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foci (-2, 3) and (4, 3) b=4
Please help me solve this. Find the general and standard form then graph it.
If it is not that much of a hassle, i would also appreciate it so much if it has a solution.
This is all about ellipse. This is the equation that i ended up with
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The method of analysis is close to what I showed you for similar problem under this link
https://www.algebra.com/algebra/homework/Quadratic-relations-and-conic-sections/Quadratic-relations-and-conic-sections.faq.question.1187463.html
https://www.algebra.com/algebra/homework/Quadratic-relations-and-conic-sections/Quadratic-relations-and-conic-sections.faq.question.1187463.html
The foci lie on the horizontal line y= 3 --- hence, the major axis of the ellipse is HORIZONTAL.
The center of the ellipse is the point (1,3) --- it explains the numbers in the equation of the ellipse.
Further, the distance between the foci is 4 - (-2) = 6 units; hence, the eccentricity of the ellipse is c = = 3 units.
Now you know "c" and "b" of the ellipse: c = 3, b = 4 (given). (As a reminder: b is the minor semi-axis).
You are in position to find the major semi-axis a = = = = 5.
After that, the equation of the ellipse is
+ = .
Solved, and everything is explained.
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For basic info about ellipses, see my lesson
- Ellipse definition, canonical equation, characteristic points and elements
in this site.