Question - Circle Equation with Center and Radius
Solution:
The equation given in the image is for a circle, and it is written in the standard form:\[ (x - h)^2 + (y - k)^2 = r^2 \]where $$(h, k)$$ is the center of the circle, and $$r$$ is the radius.The given equation is:\[ (x - 3)^2 + (y - 1)^2 = 4 \]From this equation, we can directly read the center and the radius of the circle:Center $$(h, k)$$ is $$(3, 1)$$, as it's the point you get by undoing the sign change in the brackets.Radius $$r$$ is $$\sqrt{4}$$, which is $$2$$, as the radius squared $$r^2$$ equals $$4$$.So the center of the circle is at the point $$(3, 1)$$, and the radius is $$2$$. To represent this graphically, you would plot the center at point $$(3, 1)$$ on a Cartesian plane and draw a circle around this point with a radius of $$2$$ units, ensuring that all points on the circumference of the circle are $$2$$ units away from the center.
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