SOLUTION: what is the length of the major axis of (x+2)^2 + 2(y-2)^2 = 49 i think you divide both sides by 49 but after that i am lost thank you

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: what is the length of the major axis of (x+2)^2 + 2(y-2)^2 = 49 i think you divide both sides by 49 but after that i am lost thank you      Log On


   

Question 323848: what is the length of the major axis of (x+2)^2 + 2(y-2)^2 = 49
i think you divide both sides by 49 but after that i am lost
thank you
Found 2 solutions by rapaljer, jim_thompson5910:
Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
You are correct to divide both sides by 49, in order to set the equation equal to 1. Then, in the y portion of the equation, you have to invert the 2 coefficient. So in this ellipse, a^2=49 and b^2 = 49/2. The larger of these two is a=7, so the major diameter is 14.

Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Divide everything by 49 to get %28%28x%2B2%29%5E2%29%2F49+%2B+%282%28y-2%29%5E2%29%2F49+=+1 and rewrite 2%2F49 as 1%2F%2849%2F2%29 to get


%28%28x%2B2%29%5E2%29%2F49+%2B+%28%28y-2%29%5E2%29%2F%2849%2F2%29+=+1


Now rewrite 49 as 7%5E2 and 49%2F2 as %287%2Fsqrt%282%29%29%5E2 to get





Now the equation is in the form %28x-h%29%5E2%2Fa%5E2%2B%28y-k%29%5E2%2Fb%5E2=1 where a=7 and b=7%2Fsqrt%282%29


Since a=7 is the larger of the two, this means that the length of the semi-major axis is 7 units. Double this to get 7*2=14.


So the length of the major axis is 14 units long.