SOLUTION: 64x^2 + 25y^2 = 6400 The major axis has length? The minor axis has length? x^2/(100) + y^2/(49) = 1 Length of major axis? Length of minor axis? Thank you

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: 64x^2 + 25y^2 = 6400 The major axis has length? The minor axis has length? x^2/(100) + y^2/(49) = 1 Length of major axis? Length of minor axis? Thank you      Log On


   

Question 949353: 64x^2 + 25y^2 = 6400
The major axis has length?
The minor axis has length?

x^2/(100) + y^2/(49) = 1
Length of major axis?
Length of minor axis?
Thank you
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
Major axis: The longest diameter of an ellipse.
Minor axis: The shortest diameter of an ellipse.
recall:
x%5E2%2Fa%5E2+%2B+y%5E2%2Fb%5E2+=+1....the horizontal major axis
x%5E2%2Fb%5E2+%2B+y%5E2%2Fa%5E2+=+1....the vertical major axis

1.
64x%5E2+%2B+25y%5E2+=+6400...first write it in x%5E2%2Fa%5E2+%2B+y%5E2%2Fb%5E2+=+1 form
64x%5E2%2F6400+%2B+25y%5E2%2F+6400=+6400%2F6400
x%5E2%2F100+%2B+y%5E2%2F256=+1 =>here we have the vertical major axis and the a%5E2 lies under y and b%5E2 under x
b%5E2=100 => b=10
a%5E2=256 => a=16
so,
the major axis has length: => a=16
the minor axis has length: => b=10



2.
x%5E2%2F%28100%29+%2B+y%5E2%2F%2849%29+=+1 =>here we have the horizontal major axis and the a%5E2 lies under x and b%5E2 under y
a%5E2=100 => a=10
b%5E2=49 => b=7
Length of major axis is: a+=10
Length of minor axis is: b+=7