The equation of a circle that has a radius of 4/9 units and is centered at (-6.2,5.8) would be (x)² + (y)² + 12.4x - 11.6y + 72.27 = 0.
What is the general equation of a circle?
The general equation of a circle of radius r represents all the points that lie on the circumference of the given circle.
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the center and r is the radius
It is given that a circle has a radius of 4/9 units and is centered at (-6.2,5.8)
here (h, k ) = (- 6.2, 5.8 ) and r = 4/9 units ,
hence
(x - h)² + (y - k)² = r²
(x + 6.2)² + (y - 5.8)² = (4/9 )²
(x + 6.2)² + (y - 5.8)² = 16/81
(x)² + (y)² + 38.44 + 12.4x + 33.64 - 11.6y = 16/81
(x)² + (y)² + 12.4x - 11.6y + 72.27 = 0
Thus the equation of a circle is (x)² + (y)² + 12.4x - 11.6y + 72.27 = 0
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