SOLUTION: Please help me with this I've never heard of these nor have I done these. Find the length of the major and minor axes for this ellipse.? 1.) (x^2/16)+(y^2/25) 2.) (x^2/10

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Question 472765: Please help me with this I've never heard of these nor have I done these.
Find the length of the major and minor axes for this ellipse.?
1.) (x^2/16)+(y^2/25)
2.) (x^2/100)+(y^2/25)
Find the length of the major and minor axis for this ellipse.
3.) x^2+4y^2=33

These are the 3 most difficult problems I've ever come across.
If someone can please break this down for me I would greatly appreciate it...
I've been on these for hours and keep making minor mistakes in between steps..
so much so that I have no idea where I am at... PLZ help!!!
Found 2 solutions by stanbon, ewatrrr:
Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
Find the length of the major and minor axes for this ellipse.?
1.) (x^2/16)+(y^2/25) = 1
---
Half of the major axis is sqrt(25) = 5
So, major axis is 2*5 = 10
---
Half of the minor axis is sqrt(16) = 4
So, minor axis is 2*4 = 8
===========================================
2.) (x^2/100)+(y^2/25) = 1
Similarly, major = 2*sqrt(100) = 2*10 = 20
minor = 2*sqrt(25) = 2*5 = 10
===========================================
3.) x^2+4y^2=33
---
(x^2/33) + (y^2/(33/4)) = 1
----
major = 2*sqrt(33)
minor = 2*sqrt(33)/2 = sqrt(33)
==================================
Cheers,
Stan H.
==============

Answer by ewatrrr(24785)   (Show Source): You can put this solution on YOUR website!
 

Hi,

As a tutor,use  arc(0,0,20,10) as a drawing (see source)

which instructs Ellipse with C(0,0) x-length of 20 and y-length of 10.



Using a graphing software one would need to use-solving for y: for ex in(1

 y =  5*sqrt(1-x^2/16) and y = -5*sqrt(1-x^2/16)

 

 Standard Form of an Equation of an Ellipse is 

where Pt(h,k) is the center and a and b  are the respective vertices distances from center.

 Below all with centers at P(0,0)

Lengths of the Axis are 2a and 2b with the Major Axis being the LONGEST of the two

1.) (x^2/16)+(y^2/25)= 1 Major = 2*5 = 10units and Minor = 2*4 = 8units 

2.) (x^2/100)+(y^2/25)= 1  Major = 2*10 = 100units and Minor = 2*5 = 10units 

3.) x^2+4y^2=33 

   x^2/33 +y^2/8.25 = 1   Major = 2*sqrt(33)  and Minor = 2*sqrt(8.25)





 

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