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

Algebra ->  Quadratic-relations-and-conic-sections -> 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      Log On


   

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) About Me  (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) About Me  (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 %28x-h%29%5E2%2Fa%5E2+%2B+%28y-k%29%5E2%2Fb%5E2+=+1+

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

%28x%29%5E2%2Fa%5E2+%2B+%28y%29%5E2%2Fb%5E2+=+1+ 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)