This program is Copyright © 1978 by HewlettPackard and is used here by permission. This program was originally published in "HP33E Mathematics Applications".
This program is supplied without representation or warranty of any kind. HewlettPackard Company and The Museum of HP Calculators therefore assume no responsibility and shall have no liability, consequential or otherwise, of any kind arising from the use of this program material or any part thereof.
This program calculates the point of intersection (x_{p}, y_{p}) of two lines, each of them is specified by two points i.e., (x_{1}, y_{1}), (x_{1}', y_{1}') and (x_{2}, y_{2}), (x_{2}', y_{2}'). x_{p} and y_{p} are calculated from the equation of straight line y = x tan + c. i.e. by solving:
 1 tan theta1   y_{p}   c_{1}   1 tan theta2   x_{p}  =  c_{2} 
"Error 0" will be displayed if two lines have the same slope, i.e. if they are either parallel or overlapping.
Step 
Instructions 
Input Data/Units 
Keys 
Output Data/Units 
1 
Enter program 

2 
Input the first line by two points 
x_{1} 
ENTER 


x_{1}' 
ENTER 


y_{1} 
ENTER 




y_{1}' 
GSB 01 
C_{1} 
3 
Input the 2^{nd} line by two points and calculate the intersection. 
x_{2} 
ENTER 



x_{2}' 
ENTER 



y_{2} 
ENTER 

y_{2}' 
GSB 10 
x_{p} 

R/S 
y_{p} 

4 
For a new pair of lines, go to step 2. 


Find the intersection of the lines defined by the points (4, 8), (1, 2) and (3, 9), (7, 1).
Solution:
x_{p} = 4, y_{p} = 2 Keystrokes Display 4 ENTER 1 CHS ENTER 8 ENTER 2 CHS GSB 01 0.0000 3 CHS ENTER 7 ENTER 9 ENTER 1 CHS GSB 10 4.0000 R/S 2.0000
LINE CODE KEYS 00 f CLEAR PRGM 01 12 37 GSB 37 02 23 3 STO 3 03 24 2 RCL 2 04 24 1 RCL 1 05 24 3 RCL 3 06 61 x 07 41  08 23 4 STO 4 09 74 R/S 10 12 37 GSB 37 11 23 5 STO 5 12 24 2 RCL 2 13 24 1 RCL 1 14 24 5 RCL 5 15 61 x 16 41  17 23 6 STO 6 18 24 4 RCL 4 19 41  20 24 3 RCL 3 21 24 5 RCL 5 22 41  23 23 7 STO 7 24 71 ÷ 25 74 R/S 26 24 4 RCL 4 27 24 5 RCL 5 28 32 CHS 29 61 x 30 24 3 RCL 3 31 24 6 RCL 6 32 61 x 33 51 + 34 24 7 RCL 7 35 71 ÷ 36 74 R/S 37 23 1 STO 1 38 41  39 23 0 STO 0 40 22 Roll dn 41 23 2 STO 2 42 41  43 24 0 RCL 0 44 15 4 g >P 45 22 Roll dn 46 14 9 f TAN 47 15 12 g RTN
R0 used R1 x_{1}', x_{2}' R2 y_{1}', y_{2}' R3 tan_{1} R4 c_{1} R5 tan_{2} R6 C_{2} R7 Det
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