Three points on a circle are given in an input file: x y 11.5 5 3.2 8.6 -4.5 -6.8The equation of a circle with radius R and center at (x0, y0) is given by:(x – x0)2 + (y-y0)2 = R2The equation can also be written in the form:-2x0x – 2y0y + c = -(x2 + y2) where c = x02 + y02 – R2Given the coordinates of three points (x1, y1), (x2, y2) and (x3, y3) 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 x0, y0 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: x y 11.5000 5.0000 3.2000 8.6000 -4.5000 -6.80003.8213 -1.3356 center9.9550 radiusThe original points are shown in columns in the output file which are 15 characters wide with no space in between them. Be sure to prompt for the output filename.Someone please help with this. Do it in MATLAB.very very urgent.

Answered: The equation can also be written in the…

EBK JAVA PROGRAMMING

9th Edition

ISBN:9781337671385

Author:FARRELL

Publisher:FARRELL

Chapter13: File Input And Output

Section: Chapter Questions

Problem 20RQ

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Question

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

x y

11.5 5

3.2 8.6

-4.5 -6.8

The equation of a circle with radius R and center at (x₀, y₀) is given by:

(x – x₀)² + (y-y₀)² = R²

The equation can also be written in the form:

-2x₀x – 2y₀y + c = -(x² + y²) where c = x₀² + y₀² – R²

^{Given the coordinates of three points (x₁, y₁), (x₂, y₂) and (x₃, y₃) 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 x₀, y₀ 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:}

x y

11.5000 5.0000

3.2000 8.6000

-4.5000 -6.8000

3.8213 -1.3356 center

9.9550 radius

The original points are shown in columns in the output file which are 15 characters wide with no space in between them. Be sure to prompt for the output filename.

Someone please help with this. Do it in MATLAB.very very urgent.

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