How I plot parametric ellipse ,, tangenten and perpendicular.?

1)Give ellipse (x-1)^2+y^2/4=1 after some calculation I got x= cost +1 y= 2sint (parametric equations)

2)Find a unit tangent vector, parametric equations of the tangent and perpendicular in point (1, 2). after some calculation I got unit tangent vector (1,2) tangent (0,-2) perpendicular (1,0)

I got the matlab code from lecture but I try to changes the equations to mine but is not work.

close all % Approximation of an ellipse (parametrized!) (x/2)^2+(y/3)^2=1. for i=5:10 % define the parameter t t = 0:2*pi/i:2*pi; % plot parametric curve plot(sqrt(cos(t)+1)), sqrt(2)*sin(t); axis equal; xlim([-2,2]); ylim([-2,2]); % set a grid on the plot grid on; title(sprintf('Approximation of the ellipse (x/2)^2+(y/3)^2=1 with i = %i', i)); pause(1); end

If somebody have better and easier solution please give me advice..

thank you!

[Ramesh Bala]

%parametric form

t = linspace(0, 2*pi, 200);

xt = r1 * cos(t) + xc; yt = r2 * sin(t) + yc;

% aply rotation by angle theta

cot = cos(theta); sit = sin(theta);

x = xt * cot - yt * sit;

y = xt * sit - yt * cot;

plot(x, y, '-');

Answer 1

[Ajey Pandey]

To piggyback off Kaleesh's comment, the documentation for plot offers a tutorial for plotting parametric equations.

https://www.mathworks.com/help/matlab/ref/plot.html

Look for the "Plot Circle" example.

[Ramesh Bala]

yeah thanks in circle case it's same radii and axis equal.In ellipse r varies.So,if one knows r1 ,using formulation can get r2.

So any idea to get r1 from foci?