SOLUTION: Find the length of the major axis for the graph of 49x^2 + 16y^2 = 784 I'm struggling with this one. Any help would be appreciated. Thank you Michele

Algebra ->  Algebra  -> Quadratic-relations-and-conic-sections -> SOLUTION: Find the length of the major axis for the graph of 49x^2 + 16y^2 = 784 I'm struggling with this one. Any help would be appreciated. Thank you Michele       Log On

Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!
Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations!

   

Question 170009: Find the length of the major axis for the graph of 49x^2 + 16y^2 = 784
I'm struggling with this one. Any help would be appreciated.
Thank you
Michele

Answer by jim_thompson5910(21685) About Me  (Show Source):
You can put this solution on YOUR website!
49x%5E2+%2B+16y%5E2+=+784 Start with the given equation


%2849x%5E2+%2B+16y%5E2%29%2F784+=+cross%28784%2F784%29 Divide both sides by 784. The goal here is to make the right side equal to 1


%2849x%5E2+%2B+16y%5E2%29%2F784+=+1 Simplify


%2849x%5E2%29%2F784+%2B+%2816y%5E2%29%2F784+=+1 Break up the fraction


%28x%5E2%29%2F16+%2B+%28y%5E2%29%2F49+=+1 Reduce


%28x%5E2%29%2F%284%5E2%29+%2B+%28y%5E2%29%2F%287%5E2%29+=+1 Rewrite 16 as 4%5E2. Rewrite 49 as 7%5E2


Now the equation is in the form %28%28x-h%29%5E2%29%2F%28a%5E2%29+%2B+%28%28y-k%29%5E2%29%2F%28b%5E2%29+=+1 where h=0, k=0, a=4, and b=7.


The values of "a" and "b" are the lengths of the major and minor axis. If "a" is larger than "b", then 2a is the length of the major axis. On the other hand, if "b" is larger than "a", then 2b is the length of the major axis.


Since b%3Ea, this means that the length of the major axis is 2b.


So multiply the value of "b" by 2 to get 2%2A7=14



So the length of the major axis is 14 units