1  REM  ****  HP BASIC PROGRAM LIBRARY  *******************************
2  REM
3  REM        PARABO:   FINDS THE EQUATION OF THE PARABOLA PASSING
4  REM                  THROUGH 3 GIVEN POINTS
5  REM        36702 REV  A   10/73
6  REM
7  REM  ****  CONTRIBUTED PROGRAM  ************************************
10  REM ***** PARABO ***** MATHEMATICS PROGRAM
20  REM ***** FINDS EQUATION OF PARABOLA PASSING THORUGH THREE POINTS
30  DIM P$[9],Q$[9]
35  LET P$=" POINT"
100  PRINT "THIS PROGRAM FINDS THE EQUATION OF A PARABOLA PASSING THROUGH"
110  PRINT "THREE";P$;"S.  YOU ENTER THE X AND Y COORDINATES OF EACH";P$;"."
160  PRINT '10"FIRST";P$;
170  INPUT X1,Y1
180  PRINT "SECOND";P$;
190  INPUT X2,Y2
200  PRINT "THIRD";P$;
210  INPUT X3,Y3
230  LET D=X2*X1^2+X1*X3^2+X3*X2^2-X3*X1^2-X1*X2^2-X2*X3^2
240  IF D=0 THEN 325
250  LET A=(Y1*(X2-X3)+Y2*(X3-X1)+Y3*(X1-X2))/D
260  LET B=(Y1*(X3^2-X2^2)+Y2*(X1^2-X3^2)+Y3*(X2^2-X1^2))/D
270  LET F1=X3*X2^2-X2*X3^2
280  LET F2=X1*X3^2-X3*X1^2
290  LET F3=X2*X1^2-X1*X2^2
300  LET C=(Y1*F1+Y2*F2+Y3*F3)/D
310  PRINT '10"THE EQUATION IS:  Y =";A;"X^2 +";B;"X +";C
320  GOTO 410
325  PRINT '10"THE EQUATION FOR THESE";P$;"S IS NOT A FUNCTION";
330  IF X1#X2 THEN 390
340  IF X2#X3 THEN 390
360  PRINT "."'13'10"IT HAS THE FORM  X =";X1
370  GOTO 410
390  PRINT "AND THE COEFFICIENTS CANNOT BE DETERMINED BY THIS PROGRAM."
410  PRINT '10'10"DO YOU WISH TO RUN AGAIN";
450  INPUT Q$
460  IF Q$>"Y" THEN 160
470  END 
