SOLUTION: Pls help me solve : given the with equation 25x^2+16y^2=400 .find the i) length of the major axis,ii)the length of the minor axis,iii) eccentricity, iv)coordinate of the foci,v)

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Question 1095275: Pls help me solve : given the with equation 25x^2+16y^2=400 .find the i) length of the major axis,ii)the length of the minor axis,iii) eccentricity, iv)coordinate of the foci,v) coordinates of the vertices,vi) the coordinate of the directrices,vii)the latus rectum of the ellipse.

Answer by ikleyn(52800)   (Show Source): You can put this solution on YOUR website!
.
You are given

 = 400.


Divide by 400 both sides.  You will get

 +  = 1,    or, which is the same

 +  = 1,    or,  which is the same


 +  = 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  =  =  = 3.


The foci are  (0,3)  and  (0,-3).

----------------
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

    - OVERVIEW of lessons on ellipses


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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