Lets first try to find the slope between the two points. Note, if the slope is 0, then the line would be a horizontal line. If the slope is undefined, then it is a vertical line.
We can use the slope formula to find the slope between the two lines, but notice something. The slope formula is technically just the change in y divided by the change in x. Between the two points, the y-value does not change and the x-value does change. This means that the change in y is 0, but the change in x is not zero. This means that the slope would be 0, resulting in a horizontal line.
Now, we know that the resulting line is horizontal, meaning it will take the form of y = _. Since the y-values for both of the points is 6, it makes sense to say that the equation for the line would be y = 6.
(a) When the circle is offset from the origin, the equation for the radius gets messy. In general, it will be the root of a quadratic equation in sine and cosine, not easily simplified. The Cartesian equation is easier to write.
Circle centered at (h, k) with radius r:
(x -h)^2 +(y -k)^2 = r^2
The given circle is ...
(x -2)^2 +(y -2)^2 = 16
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(b) When the circle is centered at the origin, the radius is a constant. The desired circle is most easily written in polar coordinates: