SOLUTION: What is the center, foci and the length of the major and minor axes' of: 7x^2 + 3y^2 - 28x - 12y = -19 And also how would you graph this?

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: What is the center, foci and the length of the major and minor axes' of: 7x^2 + 3y^2 - 28x - 12y = -19 And also how would you graph this?      Log On


   

Question 444190: What is the center, foci and the length of the major and minor axes' of:
7x^2 + 3y^2 - 28x - 12y = -19
And also how would you graph this?
Answer by poliphob3.14(115) About Me  (Show Source):
You can put this solution on YOUR website!
We complete the square for x and y on the left side by adding 28+12 on both sides:
7x%5E2-28x%2B3y%5E2-12y=-19=> 7%28x%5E2-4x%2B4%29%2A3%28y%5E2-4y%2B4%29=-19%2B28%2B12=>
7%28x-2%29%5E2%2B3%28y-2%29%5E2=21, divide both sides by 21
%28x-2%29%5E2%2F3%2B%28y-2%29%5E2%2F7=1, that is the equation of ellipse with center (2, 2),
major axis 2sqrt%287%29, minor axis 2sqrt%283%29,
and foci [ c%5E2=7%5E2-3%5E2=40 => c=2sqrt%2810%29] the points:
(2, 2%2B2sqrt%2810%29) and (2, 2-2sqrt%2810%29).
.