**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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