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X² - 2x+8y = 55-4x-y²; diameter​

User DarkAjax
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1 Answer

4 votes

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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X² - 2x+8y = 55-4x-y²; diameter​-example-1
User Lucas Ross
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