SOLUTION: Find the length of the major axis for the graph of 49x2 + 16y2 = 784

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Question 170007: Find the length of the major axis for the graph of 49x2 + 16y2 = 784
Answer by Edwin McCravy(6941) About Me  (Show Source):
You can put this solution on YOUR website!
49x%5E2+%2B+16y%5E2+=+784

Get it in one of these forms, a%3Eb

x%5E2%2Fa%5E2+%2B+y%5E2%2Fb%5E2=1 if it is an ellipse that
looks like this:

drawing%28100%2C100%2C-2.2%2C2.2%2C-2.2%2C2.2%2C+graph%28100%2C100%2C-2.2%2C2.2%2C-2.2%2C2.2%2Csqrt%28%281-x%5E2%29%2F2%29%29%2C%0D%0Agraph%28100%2C100%2C-2.2%2C2.2%2C-2.2%2C2.2%2C-sqrt%28%281-x%5E2%29%2F2%29%29+%29

or x%5E2%2Fb%5E2+%2B+y%5E2%2Fa%5E2=1 if it is an ellipse that
looks like this:

drawing%28100%2C100%2C-2.2%2C2.2%2C-2.2%2C2.2%2C+graph%28100%2C100%2C-2.2%2C2.2%2C-2.2%2C2.2%2Csqrt%281-4x%5E2%29%29%2C%0D%0Agraph%28100%2C100%2C-2.2%2C2.2%2C-2.2%2C2.2%2C-sqrt%281-4x%5E2%29%29+%29




Get a 1 on the right by dividing every term by 784

49x%5E2%2F784+%2B+16y%5E2%2F784+=+784%2F784

x%5E2%2F16+%2B+y%5E2%2F49+=+1

Since the larger denominator is under y%5E2, this
is an ellipse of the second type above:

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

So a%5E2=49 and so a=7

The major axis has length 2a

so the answer to your problem is 

major_axis=2a=2%287%29+=+14

Its graph is:

drawing%28400%2C400%2C-8%2C-8%2C-8%2C8%2C+graph%28400%2C400%2C-8%2C8%2C-8%2C8%2Csqrt%28784-49x%5E2%29%2F4%29%2C%0D%0Agraph%28400%2C400%2C-8%2C8%2C-8%2C8%2C-sqrt%28784-49x%5E2%29%2F4%29+%29

Edwin