Question 1082536
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<pre>
The figure is an ellipse     ("the locus of a point which moves so that the summation of its distance from two given points is constant").


The major axis is the line y = 2 parallel to x-axis.


The major semi-axis length is half of that distance of 5 units, i.e. a= 2.5 units.


The distance between foci is 1 - (-2) = 3.
So, the linear eccentricity is half of that, i.e. c= 1.5.


Find the minor semi-axis length "b" from the equation {{{c^2}}} = {{{a^2 - b^2}}}:

b = {{{sqrt(2.5^2-1.5^2)}}} = 2.


Now the equation of the ellipse is 

{{{x^2/2.5^2}}} + {{{y^2/2^2}}} = 1.
</pre>

See the lesson

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Quadratic-relations-and-conic-sections/Ellipse-definition--canonical-equation--characteristic-points-and-elements.lesson>Ellipse definition, canonical equation, characteristic points and elements</A>

in this site.


Also, &nbsp;you have this free of charge online textbook in ALGEBRA-II in this site

&nbsp;&nbsp;&nbsp;&nbsp;<A HREF=https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-II - YOUR ONLINE TEXTBOOK</A>.


The referred lesson is the part of this online textbook under the topic 
"<U>Conic sections: Ellipses. Definition, major elements and properties. Solved problems</U>".