The diameter of the equation of a circle in the xy-plane as shown is 26 units.
The standard form for finding the equation of a circle is expressed as:
[tex]x^2 + y^2 +2gx + 2fy +C= 0[/tex]
For us to get the diameter of the circle, we need to get the radius of the circle first calculated as shown:
[tex]r=\sqrt{g^2+f^2-C}[/tex]
Given the equation of the circle expressed as [tex]x^2 + y^2 - 6x + 8y = 144[/tex]
Compare with the general formula:
2gx = -6x
g = -6/2
g = -3
Similarly;
2fy = 8y
2f = 8
f = 4
C = -144
Substitute into the formula for calculating the radius;
[tex]r=\sqrt{(-3}^2+4^2-(-144)\\r=\sqrt{9+16+144}\\r=\sqrt{169}\\r=13units[/tex]
Get the diameter of the circle
d = 2r
d = 2(13)
d = 26 units
Hence the diameter of the equation of a circle in the xy-plane as shown is 26 units.
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