The diameter at the center of the tower is_ meters. the center of the tower is _meters above the ground

think 5 meters

Step-by-step explanation:

The diameter at the center of the tower is 4 meters. The center of the tower is 8 meters above the ground.

Step-by-step explanation:

4x^2-y^2+16y-80=0

Completing squares in variable "y": Common factor -1:

4x^2-(y^2-16y)-80=0

4x^2-[(y-16/2)^2-(16/2)^2]-80=0

4x^2-[(y-8)^2-(8)^2]-80=0

4x^2-[(y-8)^2-64]-80=0

Eliminating the brackets:

4x^2-(y-8)^2+64-80=0

Adding like terms (constants):

4x^2-(y-8)^2-16=0

Adding 16 both sides of the equation:

4x^2-(y-8)^2-16+16=0+16

4x^2-(y-8)^2=16

Dividing all the terms by 16:

4x^2/16-(y-8)^2/16=16/16

Simplifying:

x^2/4-(y-8)^2/16=1

The hyperbola has the form:

(x-h)^2/a^2-(y-k)^2/b^2=1

Then:

h=0

k=8

a^2=4→sqrt(a^2)=sqrt(4)→a=2

The diameter (d) at the center of the tower is:

d=2a→d=2(2)→d=4 meters

The center of the tower is 8 (k) meters above the ground.

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step-by-step explanation: