SOLUTION: For the given ellipse, find the principal axis, center, vertices, co-vertices, foci, length of the major axis and length of minor axis 5y^2+2x^2=10 (x+2)^2/25+(y+5)^2=1

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: For the given ellipse, find the principal axis, center, vertices, co-vertices, foci, length of the major axis and length of minor axis 5y^2+2x^2=10 (x+2)^2/25+(y+5)^2=1       Log On


   

Question 1166895: For the given ellipse, find the principal axis, center, vertices, co-vertices, foci, length of the major axis and length of minor axis
5y^2+2x^2=10
(x+2)^2/25+(y+5)^2=1
Answer by Edwin McCravy(20059) About Me  (Show Source):
You can put this solution on YOUR website!
5y%5E2%2B2x%5E2=10

becomes 

x%5E2%2F5%5E%22%22%2By%5E2%2F2%5E%22%22=1

x%5E2%2F%28sqrt%285%29%29%5E2%2By%5E2%2F%28sqrt%282%29%29%5E2=1

principal axis = x=axis  (y=0)
center = (0,0)
vertices = (±√5,0)
co-vertices = (0,±√2)
foci = (±√3,0)
length of the major axis = 2√5 
length of minor axis = 2√2

graph:


----------------------------
%28x%2B2%29%5E2%2F25%2B%28y%2B5%29%5E2=1

%28x%2B2%29%5E2%2F5%5E2%2B%28y%2B5%29%5E2%2F1%5E2=1

principal axis y=-5
center = (-2,-5)
vertices = (-7,-5), (3,-5)
co-vertices = (-2,-6), (-2,-4)
foci = (-2√(6)±2,-5)
length of the major axis = 10 
length of minor axis = 2

graph:
drawing%28400%2C1000%2F3%2C-8%2C4%2C-8%2C2%2Cgrid%281%29%2Carc%28-2%2C-5%2C10%2C-2+%29%29

Edwin