PLEASE EXPLAIN BEGINNING AT A = WHAT ARE WE DOING THIS IS C++ #include <iostream

Question

PLEASE EXPLAIN BEGINNING AT A = WHAT ARE WE DOING THIS IS C++

#include <iostream>

#include <cmath>

using namespace std;

int main()
{

    double m, c, r, a, b;
    double A, B, C, d;
    double x1, x2, y1, y2;

    // get data
    cout << "Enter the slope of the line: ";
    cin >> m;
    cout << "Enter the y-inter of line: " ;
    cin >> c;
    cout << "Enter the x-value of the center of circle: ";
    cin >> a;
    cout << "Enter the y-value of the center of circle: ";
    cin >> b;
    cout << "Enter the radius of circle: ";
    cin >> r;

    // compute intersection equations

     A = pow(m,2) + 1;
     B = -2*a + 2*(c-b)*m;
     C = pow(a,2) + pow((c-b),2) - pow(r,2);
     d = pow(B,2) - 4*A*C;

     x1 = (-B - sqrt(d))/(2*A);
     x2 = (-B + sqrt(d))/(2*A);

     y1 = m*x1 + c;
     y2 = m*x2 + c;

     cout << "The intersection points are (" << x1 << "," << y1 << ") and ("
                << x2 << "," << y2 << ")." << endl;



    return 0;
}

Explanation / Answer

//The process is mentioned in comments
#include<conio.h>
#include <iostream>
#include <cmath>

using namespace std;

int main()
{

double m, c, r, a, b;
double A, B, C, d;
double x1, x2, y1, y2;

// get data
   // accepts the data from user
cout << "Enter the slope of the line: ";
cin >> m; //let us suppose the user entered 5
cout << "Enter the y-inter of line: " ;
cin >> c; //let us suppose the user entered 2
cout << "Enter the x-value of the center of circle: ";
cin >> a; //let us suppose the user entered 3
cout << "Enter the y-value of the center of circle: ";
cin >> b; //let us suppose the user entered 1
cout << "Enter the radius of circle: ";
cin >> r; //let us suppose the user entered 5

// compute intersection equations

// calculate pow(m,2)+1 and assigns it to A
   // pow(m,2) gives m to the power of 2
A = pow(m,2) + 1; //for the given values A will be 26

   // calculate -2*a + 2*(c-b)*m and assign it to B
B = -2*a + 2*(c-b)*m; // for the given values B will be 4

   // calculate pow(a,2) + pow((c-b),2) - pow(r,2) and assign it to C
C = pow(a,2) + pow((c-b),2) - pow(r,2); //for the given values C will be -15

   // calculate pow(B,2) - 4*A*C and assign it to d
d = pow(B,2) - 4*A*C; // for the given values d will be 1576

   // calculate (-B - sqrt(d))/(2*A) and assign it to x1
   //sqrt(d) gives the squareroot of d
x1 = (-B - sqrt(d))/(2*A); // for the given values x1 will be -0.840363

   // calculate (-B + sqrt(d))/(2*A) and assign it to x2
x2 = (-B + sqrt(d))/(2*A); // for the given values x2 will be 0.686517

   // calculate m*x1 + c and assign it to y1
y1 = m*x1 + c; // for the given values y1 will be -2.20182

   // calculate m*x2 + c and assign it to y2
y2 = m*x2 + c; // for the given values y2 will be 5.43258

   //Finally print the intersecting points
   //The intersecting point are (x1,y1) and (x2,y2)
cout << "The intersection points are (" << x1 << "," << y1 << ") and ("<< x2 << "," << y2 << ")." << endl;

   return 0;
}

Step by step calculations:

Suppose the user enters

m = 5, c = 2, a = 3 , b = 1, r= 5

Now A= pow(m,2) + 1;

Pow(m,2) returns m to the power of 2, i.e, 5 * = 25

A = pow(m,2) + 1;

Next      B = -2*a + 2*(c-b)*m;

Which means B= (-2) * 3 + 2 * (2-1) * 5

Next      C = pow(a,2) + pow((c-b),2) - pow(r,2)

Next d = pow(B,2) - 4*A*C;

Next x1 = (-B - sqrt(d))/(2*A);

Next x2 = (-B + sqrt(d))/(2*A);

Next y1 = m*x1 + c;

Next y2 = m*x2 + c;

Finally the intersection points are (-0.840363 , -2.20181) and (0.686517,5.43258)

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