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The point of intersection between a circle and a line

Author: shiroeExecutions: 1163
TOP/Shared Formulas (Math)/Geometry

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Calculates the points of intersection between a circle and a line.
Finds the number of points of intersection and their coordinates.
The number of points of intersection is determined in the real plane (xy).
This is based on the discriminant.
The coordinates of the points of intersection are the solutions to a system of equations.
These are output as complex numbers.
Please pay close attention
to ensure that the imaginary unit i is not appended to the end of the output field.

Let the equation of the circle be
(x-a)^2 + (y-b)^2 = r^2.
Let the equation of the line be
lx + my + n = 0.
Enter a, b, c, l, m, and n.
Assume that l and m are not both zero.
(Input restrictions: If any input violates these restrictions, no output will be generated.)
Be careful not to include the imaginary unit i at the end of the output.
a
　　The x-coordinate of the center of the circle
b
　　The y-coordinate of the center of the circle
r
　　Radius of a circle
l
　　The coefficient of x in the equation of a straight line
m
　　The y-coefficient of the equation of a straight line
n
　　The constant term in the equation of a straight line
Number of common points 　　(In the real plane xy)
x1 
y1 
x2 　　(It will be displayed even if it is the same as x1.)
y2 　　(It will be displayed even if it is the same as y1.)
R6 (2024). 10/16 (Wed)_Ver. 001.
Digit display setting: 50 digits. Digit count can be changed. Complex number calculation mode.

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