User:Pyro05x/Sandbox

$r={\frac {ab}{\sqrt {a^{2}\sin ^{2}\theta +b^{2}\cos ^{2}\theta }}}={\frac {b}{\sqrt {1-\varepsilon ^{2}\cos ^{2}\theta }}}$

a = (25/2) = 12.5

b = (10/2) = 5

e = sqrt(1-(b^2/a^2)) = sqrt(1-(25/156.25)) = sqrt(0.16) = 0.4

r(t) = (12.5*5)/sqrt((12.5sin(t))^2+(5cos(t))^2)

t	r	x	y
0	12.5	12.5	0
pi/12	10.751586084406789	10.385234672498676	2.782715243703712
2pi/12	8.219949365267865	7.118684968143744	4.109974682633932
3pi/12	6.56532164298613	4.642383454426301	4.642383454426296
4pi/12	5.625439504630121	2.812719752315062	4.871773518462232
5pi/12	5.146902837677898	1.3321164776832513	4.971526376313572
pi/2	5	0	5
7pi/12	5.146902837677896	-1.3321164776832455	4.971526376313572
8pi/12	5.625439504630117	-2.8127197523150556	4.871773518462232
9pi/12	6.565321642986127	-4.642383454426296	4.642383454426296
10pi/12	8.21994936526786	-7.118684968143738	4.109974682633933
11pi/12	10.751586084406778	-10.385234672498663	2.78271524370372
pi	12.5	-12.5	0