Answer:
12√2 ≈ 16.97 units
Explanation:
You want the diameter of the circle whose equation is ...
x² -2x +8y = 55 -4x -y²
Standard form
The equation can be rearranged to ...
x² -2x +4x +y² +8y = 55
(x +1)² +(y +4)² = 55 + 1 + 16
(x +1)² +(y +4)² = 72
Comparing this to the standard form equation for a circle with center (h, k) and radius r, we se ...
(x -h)² +(y -k)² = r²
(h, k) = (-1, -4) and r² = 72
Diameter
The diameter is twice the radius, so is ...
d = 2r = 2√72 = 12√2
The diameter of the circle is 12√2 units.
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