i mean, how to use translate in this context and still keep the circle line intersections to work?

if i change
float circleX = 200;
float circleY = 200;
to 0 and use translate(200,200) instead
before ellipse, the intersection detection don't work anymore

what need to be changed to use translate, rotate, scale etc.?

original code

1. float circleX = 200;
   float circleY = 200;
   float circleRadius = 100;
    
   float lineX1 = 350;
   float lineY1 = 350;
   float lineX2, lineY2;
    
   void setup() {
     size(400, 400);
     ellipseMode(RADIUS);
     smooth();
   }
    
   void draw() {
     background(204);
    
     lineX2 = mouseX;
     lineY2 = mouseY;
    
     if (circleLineIntersect(lineX1, lineY1, lineX2, lineY2, circleX, circleY, circleRadius) == true) {
       fill(0);
     }
     else {
       fill(255);
     }
    
     ellipse(circleX, circleY, circleRadius, circleRadius);
     line(lineX1, lineY1, lineX2, lineY2);
    
   }
    
   // Code adapted from Paul Bourke:
   // http://local.wasp.uwa.edu.au/~pbourke/geometry/sphereline/raysphere.c
   boolean circleLineIntersect(float x1, float y1, float x2, float y2, float cx, float cy, float cr ) {
     float dx = x2 - x1;
     float dy = y2 - y1;
     float a = dx * dx + dy * dy;
     float b = 2 * (dx * (x1 - cx) + dy * (y1 - cy));
     float c = cx * cx + cy * cy;
     c += x1 * x1 + y1 * y1;
     c -= 2 * (cx * x1 + cy * y1);
     c -= cr * cr;
     float bb4ac = b * b - 4 * a * c;
    
     //println(bb4ac);
    
     if (bb4ac < 0) {  // Not intersecting
       return false;
     }
     else {
       
       float mu = (-b + sqrt( b*b - 4*a*c )) / (2*a);
       float ix1 = x1 + mu*(dx);
       float iy1 = y1 + mu*(dy);
       mu = (-b - sqrt(b*b - 4*a*c )) / (2*a);
       float ix2 = x1 + mu*(dx);
       float iy2 = y1 + mu*(dy);
    
       // The intersection points
       //ellipse(ix1, iy1, 10, 10);
       //ellipse(ix2, iy2, 10, 10);
       
       float testX;
       float testY;
       // Figure out which point is closer to the circle
       if (dist(x1, y1, cx, cy) < dist(x2, y2, cx, cy)) {
         testX = x2;
         testY = y2;
       } else {
         testX = x1;
         testY = y1;
       }
       
       if (dist(testX, testY, ix1, iy1) < dist(x1, y1, x2, y2) || dist(testX, testY, ix2, iy2) < dist(x1, y1, x2, y2)) {
         return true;
       } else {
         return false;
       }
     }
   }
   

The code to detect the line-circle intersection depends on the line coordinates and the circle coordinates being in the same "coordinate-space" i.e. same origin, scale and rotation.

If you use translate/rotate/scale on the line only, then the line and circle have different co-ordinate-spaces so the code will not give a valid result.

There is no simple way that you can use translate/scale/rotate in the way you want and still be able to detect line circle intersections.

i see, is there some way to adapt this?
maybe someone has reusable example on this or something?