Write a MatLab script to plot two ellipses using the plot function

There was a similar question to this but I need to use the plot function for my task.

Task 1. I have been given 2 equations and I need to plot them in one figure using the plot function, I was wondering if anybody could help

– plot the two ellipses in one figure using MATLAB function plot only

– The plot should be clear and contains correct labelling

(x − 2)^2 + (y − 3 + 2x)^2 = 5

2 (x − 3)^2 + (y/3)^2 = 4

Task 2. I also need to find the coordinates of any intersections (there should be four) between the 2 ellipses

– Convert the intersection-finding problems into root-finding problems in the form of f (x) = 0

where all four f (x) need to be explicitly defined in the MATLAB code

– Implement Newton’s method and use it to find and print the coordinates (x, y) of all the inter-sections of the two ellipses. Note: you can use any online derivative finder to find f ′(x)

– The Newton’s method implemented should stop based on a given error margin

your MATLAB script shouldn’t use any symbolic functions such as sym, syms.

[Matt J]

I hope you realize you won't be able to delete your question once someone answers it. It will remain here for all time for anyone to browse, including your instructor.

[Ali]

Thanks for telling me. Really I'd want advice on how to plot a graph from an equation in general, I do want to answer it myself as much as I can.

Answer 1

[Matt J]

As an example, here is a way to plot an unrotated ellipse of known major/minor axis lengths a,b.

a=5; b=3; %major/minor axes
cx=10;cy=20;%center coordinates

t=linspace(0,360,1000);

plot(a/2*cosd(t) +cx , b/2*sind(t)+cy ); axis equal padded; xlabel x; ylabel y