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Orthogonal Trajectories in Matlab

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Nicholas Perez
Nicholas Perez on 23 Mar 2020
Commented: David Goodmanson on 30 Mar 2020
Hello,
I am trying to verify my anwser in Matlab.
The question given is: Find the value of the number a such that the families of curves y = (x + c) ^−1 and y = a (x + k)^1/3 are orthogonal trajectories.
I found a= 3^1/3 or cube root of 3.
I have never did anything with orthogonal trajectories in Matlab so any help is greatly appreaciated.
Regards,
Nick

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darova
darova on 25 Mar 2020
Can you be more precise? What kind of help do you need?
David Goodmanson
David Goodmanson on 30 Mar 2020
Hi Nicholas,
You can create the first curve with
x = 0:.001:5; % or whatever
y1 = (x+c).^(-1)
and do something similar for the other function y2. Then if you do plot(x,y1,x,y2) and experiment a bit with the upper and lower limits on x (one or both might need to be negative) you should be able to see the lines cross at right angles. But only if, after the plot command line, you use 'axis equal'. 'Axis equal' makes right angles look like right angles.

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