8. GEOMETRIC LOCI II 
Block :Geometry
 
8.3. CIRCUMFERENCE
Circumference of centre C and radius r is the geometric locus of the points, X, whose distance to C is r

that is  dist (X,C) = r.

1.- Use the mouse to move the point X and you will see that the distance from C to X  is always 5 when X is on the circumference.

2.- Find the equation of the circumference of centre C(-3,0) and radius r=5. 

You have to apply the expression:

  dist(X,C) = r

in order to obtain the equation of the circumference as shown in the lower part of the figure.  

Where X(x,y), C(-3,0) and r=5 

Note: The circumference will be studied further in a later unit.
8.4.  ELLIPSE
The ellipse with centres F1 and F2 and constant k, is the geometric locus of the points, X, the sum of whose lengths from the centres is k: dist(X,F1) + dist(X,F2) = k

Here we have drawn the ellipse whose centres are F1(-5,2) and F2(4,9) and k=15

 

1.-Observe how when dragging the point X with the mouse, that:  d1 + d2 = 15 for all points on the ellipse. 

To find the equation of the ellipse, it is sufficient to apply the expression:  dist(X,F1) + dist(X,F2) =15 given X(x,y), F1(-5,2) and F2(4,9)  

2.-Show that in this case the result is the following equation:  
Note: The ellipse will be studied further in a later unit.

       
           
  Ángela Núñez Castaín
 
Ministry of Education , Social Afairs and Sport. Year 2001
 
 

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