SOLUTION: identify the center, the length of major axis, and the length of the minor axis for the following ellipse. -16y+52=-2x^2-8x-y^2

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: identify the center, the length of major axis, and the length of the minor axis for the following ellipse. -16y+52=-2x^2-8x-y^2      Log On


   

Question 708198: identify the center, the length of major axis, and the length of the minor axis for the following ellipse.
-16y+52=-2x^2-8x-y^2
Answer by lwsshak3(11628) About Me  (Show Source):
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identify the center, the length of major axis, and the length of the minor axis for the following ellipse.
-16y+52=-2x^2-8x-y^2
rearrange terms
2x^2+8x+y^2-16y=-52
complete the square
2(x^2+4x+4)+(y^2-16y+64)=-52+8+64
2(x+2)^2+(y-8)^2=20
%28x%2B2%29%5E2%2F10%2B%28y-8%29%5E2%2F20=1
This is an equation of an ellipse with vertical major axis.
Its standard form:+%28x-h%29%5E2%2Fb%5E2%2B%28y-k%29%5E2%2Fa%5E2=1, a>b, (h,k)=(x,y) coordinates of center
For given ellipse:
center: (-2,8)
length of vertical major axis=2a=2√20≈8.94
length of minor axis=2b=2√10≈6.32