Sunday, July 31, 2016

Casio fx-50FH Programs: Ellipses

Casio fx-50FH Programs: Ellipses

Hello everyone!  It is good to be back.  What a crazy year this has been so far.  





Introduction

The programs assume that the center of the ellipse is (0,0).  They can be adopted on the current Casio graphing calculators and fx-5800p as well (some adjustments may be necessary).  

Casio fx-50FH Ellipse Program 1: Area, Eccentricity, Focal Points
(61 steps)

Text after double slash marks (\\) are comments.  

?→X:   \\ radius on X-axis
?→Y:   \\ radius on Y-axis
X≥Y ⇒ Goto 0:
X→B: Y→A: Goto 1:  \\ X ≥ Y 
Lbl 0: X→A: Y→B:   \\ X < Y
Lbl 1: πAB ◢  \\ calculate area
√(1 - B ² ÷ A ²) ◢   \\ calculate eccentricity 
√(A ² - B ²)  \\ focal distance 

Test 1: X = 6.63, Y = 1.86
Area:  38.74149229
Eccentricity: 0.959841462
Focal Distance: 6.36748895
Hence the focal points are (-6.36748895, 0) and (6.36748895, 0)

Test 2: X = 2.99, Y = 5.06
Area: 47.53041189
Eccentricity: 0.806738152
Focal Distance: 4.08209505
Hence the focal points are (0, -4.08209505) and (0, 4.08209505)

Casio fx-50FH Ellipse Program 2: Points on the Ellipse, and distance to center (0,0)
(54 steps)

You specify A, B, and D.  D represents the number of steps.  Degree mode is set. 

?→A: ?→B: ?→D:
Deg: For 0→M To 360 Step 360 ÷ D:  \\ set up loop
M ◢  \\ display angle 
A cos(M) → X ◢   \\ display X coordinate 
B sin(M) → Y ◢  \\ display Y coordinate
√( X ² + Y ² ) ◢  \\ distance to center
Next  \\ end loop

Test: A = 3.25, B = 2.75, D = 6
Results: (angle, X, Y, distance)
0.000, 3.250, 0.000, 3.250
60.000, 1.625, 2.382, 2.883
120.000, -1.625, 2.382, 2.883
180.000, -3.250, 0.000, 3.250
240.000, -1.625, -2.382, 2.883
300.000, 1.625, -2.382, 2.883
360.000, 3.250, 0.000, 3.250

Until next time, 

Eddie


This blog is property of Edward Shore, 2016

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