Find the equation of the circle that best fits (in the sense of least squares) the points (-1,-2), (0, 2.4), (1.1,-4), and (2.4,-1.6). Hint: The equation of an arbitrary circle is of the form x 2 + y 2 + c1x + c2y + c3 = 0 which can be rearranged as c1x + c2y + c3 = −(x 2 + y 2 ). Now for each point (xi , yi) you have one equation of the form c1xi + c2yi + c3 = −(x 2 i + y 2 i ). You want to find c1, c2 and c3 that "best" do the job.

Find the equation of the circle that best fits (in the sense of least squares) the points (-1,-2), (0, 2.4), (1.1,-4), and (2.4,-1.6). Hint: The equation of an arbitrary circle is of the form x 2 + y 2 + c1x + c2y + c3 = 0 which can be rearranged as c1x + c2y + c3 = −(x 2 + y 2 ). Now for each point (xi , yi) you have one equation of the form c1xi + c2yi + c3 = −(x 2 i + y 2 i ). You want to find c1, c2 and c3 that "best" do the job.

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Question

Find the equation of the circle that best fits (in the sense of least squares) the points (-1,-2), (0, 2.4), (1.1,-4), and (2.4,-1.6).

Hint: The equation of an arbitrary circle is of the form x 2 + y 2 + c1x + c2y + c3 = 0 which can be rearranged as c1x + c2y + c3 = −(x 2 + y 2 ). Now for each point (xi , yi) you have one equation of the form c1xi + c2yi + c3 = −(x 2 i + y 2 i ). You want to find c1, c2 and c3 that "best" do the job.

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