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

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) (Show Source): You can put this solution on YOUR website!
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

This is an equation of an ellipse with vertical major axis.
Its standard form:, 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
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