Question 323848
Divide everything by 49 to get {{{((x+2)^2)/49 + (2(y-2)^2)/49 = 1}}} and rewrite {{{2/49}}} as {{{1/(49/2)}}} to get



{{{((x+2)^2)/49 + ((y-2)^2)/(49/2) = 1}}}



Now rewrite {{{49}}} as {{{7^2}}} and {{{49/2}}} as {{{(7/sqrt(2))^2}}} to get



{{{((x+2)^2)/(7^2) + ((y-2)^2)/((7/sqrt(2))^2) = 1}}}



Now the equation is in the form {{{(x-h)^2/a^2+(y-k)^2/b^2=1}}} where {{{a=7}}} and {{{b=7/sqrt(2)}}}



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.