The equation of the circle graphed in the considered image is of radius 4 units and centered on (x,y) = (5,0) is: (x-5)^2 + y^2 = 16
What is the equation of a circle with radius r units, centered at (x,y) ?
If a circle O has radius of r units length and that it has got its center positioned at [tex](h, k)[/tex] point of the coordinate plane, then, its equation is given as:
[tex](x-h)^2 + (y-k)^2 = r^2[/tex]
For this case, from the graph given, we see that the radius of the circle is of 4 units (the center is on 5, and circumference touches on 9, the difference is 4 units, which corresponds to the length of the considered circle's radius).
Also, the circle is centered on the x-axis at value 5, and as y is 0 on x-axis,the coordinate of its center is (h,k) = (5,0)
Thus, the equation of this circle is:
[tex](x-h)^2 + (y-k)^2 = r^2\\(x-5)^2 + (y-0)^2 = 4^2\\(x-5)^2 + y^2 = 16[/tex]
Thus, the equation of the circle graphed in the considered image is of radius 4 units and centered on (x,y) = (5,0) is: (x-5)^2 + y^2 = 16
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