Maxima 5.9.0 http://maxima.sourceforge.net
Distributed under the GNU Public License. See the file COPYING.
Dedicated to the memory of William Schelter.
This is a development version of Maxima. The function bug_report()
provides bug reporting information.
(C1) eq1 : y/x=sqrt(1-a^2);

			       y	     2
(D1) 			       - = SQRT(1 - a )
			       x
(C2) eq2 : y/(1-x) = sqrt(1-b^2);

			       y	       2
(D2) 			     ----- = SQRT(1 - b )
			     1 - x
(C3) solve([eq1,eq2],[x,y]);

		     2		  2     2
	   SQRT(1 - a ) SQRT(1 - b ) + b  - 1
(D3) [[x = ----------------------------------, 
			 2    2
			b  - a

					  2    2	      2		   2
				SQRT(1 - a ) (b  - 1) + (1 - a ) SQRT(1 - b )
			    y = ---------------------------------------------]]
						    2	 2
						   b  - a
(C6) solve([eq1,eq2],[x,a]);

(D6) 				      []
(C7) solve([ y/x = u, y/(1-x) = v, a^2+u^2 = 1, b^2 + v^2 = 1], [x, a, u, v]);

		     2	     2
	   SQRT(1 - b ) y + b  - 1
(D7) [[x = -----------------------, a = 
		    2
		   b  - 1

	2  4	  2	      2	  3		  2   3	   4  2	     2  2
- SQRT(b  y  + 2 b  SQRT(1 - b ) y  - 2 SQRT(1 - b ) y  - b  y  + 4 b  y

      2	   4	  2	   2    2
 - 3 y  + b  - 2 b  + 1)/(y  + b  - 1), 

		  2				       2
		(b  - 1) y			      b  - 1
u = ----------------------------------, v = - -----------------------], 
				 2	      SQRT(1 - b) SQRT(b + 1)
    SQRT(1 - b) SQRT(b + 1) y + b  - 1

	       2       2
     SQRT(1 - b ) y + b  - 1	        2  4	  2	      2	  3
[x = -----------------------, a = SQRT(b  y  + 2 b  SQRT(1 - b ) y
	      2
	     b  - 1

	       2   3    4  2	  2  2	    2	 4      2	 2    2
 - 2 SQRT(1 - b ) y  - b  y  + 4 b  y  - 3 y  + b  - 2 b  + 1)/(y  + b  - 1), 

		  2				       2
		(b  - 1) y			      b  - 1
u = ----------------------------------, v = - -----------------------], 
				 2	      SQRT(1 - b) SQRT(b + 1)
    SQRT(1 - b) SQRT(b + 1) y + b  - 1

		 2	 2
       SQRT(1 - b ) y - b  + 1		    2  4      2		  2   3
[x = - -----------------------, a = - SQRT(b  y  - 2 b  SQRT(1 - b ) y
		2
	       b  - 1

	       2   3    4  2	  2  2	    2	 4      2	 2    2
 + 2 SQRT(1 - b ) y  - b  y  + 4 b  y  - 3 y  + b  - 2 b  + 1)/(y  + b  - 1), 

		    2				       2
		  (b  - 1) y			      b  - 1
u = - ----------------------------------, v = -----------------------], 
				   2	      SQRT(1 - b) SQRT(b + 1)
      SQRT(1 - b) SQRT(b + 1) y - b  + 1

		 2	 2
       SQRT(1 - b ) y - b  + 1		  2  4	    2	        2   3
[x = - -----------------------, a = SQRT(b  y  - 2 b  SQRT(1 - b ) y
		2
	       b  - 1

	       2   3    4  2	  2  2	    2	 4      2	 2    2
 + 2 SQRT(1 - b ) y  - b  y  + 4 b  y  - 3 y  + b  - 2 b  + 1)/(y  + b  - 1), 

		    2				       2
		  (b  - 1) y			      b  - 1
u = - ----------------------------------, v = -----------------------]]
				   2	      SQRT(1 - b) SQRT(b + 1)
      SQRT(1 - b) SQRT(b + 1) y - b  + 1
(C8) solve([ y/x = u, y/(1-x) = v, a^2+u^2 = 1, b^2 + v^2 = 1], [y, a, u, v]);

		     2		    2
(D8) [[y = SQRT(1 - b ) - SQRT(1 - b ) x, 

	    2  2      2		   2
      SQRT(b  x  - 2 b  x + 2 x + b  - 1)
a = - -----------------------------------, 
		       x

      SQRT(1 - b) SQRT(b + 1) x - SQRT(1 - b) SQRT(b + 1)
u = - ---------------------------------------------------, 
			       x

					     2		    2
v = SQRT(1 - b) SQRT(b + 1)], [y = SQRT(1 - b ) - SQRT(1 - b ) x, 

	  2  2	    2		 2
    SQRT(b  x  - 2 b  x + 2 x + b  - 1)
a = -----------------------------------, 
		     x

      SQRT(1 - b) SQRT(b + 1) x - SQRT(1 - b) SQRT(b + 1)
u = - ---------------------------------------------------, 
			       x

					     2		      2
v = SQRT(1 - b) SQRT(b + 1)], [y = SQRT(1 - b ) x - SQRT(1 - b ), 

	    2  2      2		   2
      SQRT(b  x  - 2 b  x + 2 x + b  - 1)
a = - -----------------------------------, 
		       x

    SQRT(1 - b) SQRT(b + 1) x - SQRT(1 - b) SQRT(b + 1)
u = ---------------------------------------------------, 
			     x

					       2	        2
v = - SQRT(1 - b) SQRT(b + 1)], [y = SQRT(1 - b ) x - SQRT(1 - b ), 

	  2  2	    2		 2
    SQRT(b  x  - 2 b  x + 2 x + b  - 1)
a = -----------------------------------, 
		     x

    SQRT(1 - b) SQRT(b + 1) x - SQRT(1 - b) SQRT(b + 1)
u = ---------------------------------------------------, 
			     x

v = - SQRT(1 - b) SQRT(b + 1)]]
(C9)