The equation of a circle is [tex]\rm x^2+y^2+18.6x-8.2y+90.3=0[/tex].
What is the equation of a circle?
The standard equation of a circle is given by:
[tex]\rm (x-h)^2 + (y-k)^2 = r^2[/tex]
Where (h,k) is the coordinates of the center of the circle and r is the radius.
A circle has a radius of the square root of 13 units and is centered at (-9.3,4.1).
In the given circle, radius, r = √13 units and center, (h, k) = (-9.3, 4.1).
The equation of this circle is given;
[tex]\rm (x-(-9.3))^2 + (y-4.1)^2 = \sqrt{13}^2\\\\(x+9.3)^2+(y-4.1)=13\\\\x^2+18.6x+86.49+y^2-8.2y+16.81=13\\\\x^2+y^2+18.6x-8.2y+103.0-12=0\\\\x^2+y^2+18.6x-8.2y+90.3=0[/tex]
Hence, the required equation of a circle is [tex]\rm x^2+y^2+18.6x-8.2y+90.3=0[/tex].
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