Question 1095275
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<pre>
You are given

{{{25x^2+16y^2}}} = 400.


Divide by 400 both sides.  You will get

{{{x^2/((400/25))}}} + {{{y^2/((400/16))}}} = 1,    or, which is the same

{{{x^2/16}}} + {{{y^2/25}}} = 1,    or,  which is the same


{{{x^2/4^2}}} + {{{y^2/5^2}}} = 1.     (1)


Equation (1) is the standard equation of an ellipse.


The ellipse is centered at the coordinate origin (0,0).

It has the major axis parallel to y-axis,

   so the ellipse is taller than wide.


Its major semi-axis has the length of 5 units,

while the minor semi-axis is of 4 units long.


The vertices are (0,5), (0,-5),   (-3,0), (3,0).


The linear eccentricity of the ellipse is {{{sqrt(5^2-4^2)}}} = {{{sqrt(25-16)}}} = {{{sqrt(9)}}} = 3.


The foci are  (0,3)  and  (0,-3).
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See the lessons

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://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> 


&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Quadratic-relations-and-conic-sections/Standard-equation-of-an-ellipse.lesson>Standard equation of an ellipse</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Quadratic-relations-and-conic-sections/Identify-elements-of-an-ellipse-given-by-its-standard-eqn.lesson>Identify elements of an ellipse given by its standard equation</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Quadratic-relations-and-conic-sections/Find-a-standard-equation-of-an-ellipse-given-by-its-elements.lesson>Find the standard equation of an ellipse given by its elements</A>


&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Quadratic-relations-and-conic-sections/REVIEW-of-lessons-on-ellipses.lesson>OVERVIEW of lessons on ellipses</A> 



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>".



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.