Solve using matlab

Find a Circle

Three points on a circle are given in an input file:

The equation of a circle with radius $R$ and center at $(x_0,y_0)$ is given by:

$(x-x_0{)}^2+(y-y_0{)}^2=R^2$

The equation can also be written in the form:

$-2x_{0}x-2y_{0}y+c=-(x^2+y^2)$ where $c=x_0^2+y_0^2-R^2$

Given the coordinates of three points $(x_1,y_1),(x_2,y_2)$ and $(x_3,y_3)$ it is possible to determine the radius

and the coordinates of the center of the circle that passes through the three points. This is done by

substituting the coordinate of each of the points in the equation and solving the system of three linear

equations for $x_0,y_0$ and $c.$

Write a script which can read an input file in the format shown above. Prompt for the input filename.

Calculate the center and radius. Then the write the original coordinates of the three points, the center

and radius into an output file having this format:

The original points are shown in columns in the output file first, followed by the center, followed by the

radius. All numbers are printed in a field of $15$ character with $4$ digits after the decimal. There is one

space between the $x$ and $y$ fields for the data and for the center. The center and radius have the strings

"center" and "radius" printed after the numbers, separated from the numbers by one spaced, as shown.

Be sure to prompt for the output filename.

x y

$11.55$

$3\mathrm{.}28\mathrm{.}6$

$-4\mathrm{.}5-6$