Find the value of a

I am trying to solve this in MATLAB.

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.

Here are the steps I took to solve the problem however I can't figure out how to do this in MATLAB.

Step 1.

y’= -1(x + c)-2(1) = -1(1 / (x + c)2

Step 2.

y’= - 1/(x0+c)2

Step 3.

y’= a/3 (x + k)-2/3 (1) = a / 3(x + k)2/3

Step 4.

y’= a/ 3(x0+k)2/3

Step 5

y = a(-k+k)1/3 = a(0) = 0

Step 6

(- 1/(x0+c)2) (a/3(x0+k)2/3) = -1, a = 3(x0+c)2(x0+k)2/3

Step 7

(x0+c)-1= a(x0+k)1/3, 1/(x0+c) = a(x0+k)1/3, (x0+c) = 1/a(x0+k)1/3

Step 8

a = 3(1/a(x0+k)1/3)2(x0+k)2/3

a = 3(1/a2(x0+k)2/3) (x0+k)2/3

a = 3(1/a2)

a3 = 3 a = 3sqrt(3)

Answer 1

[Sumeet Singh]

First, create symbolic variables using syms. Then, define all the equations and find value of desired variable using solve.

[Trenton Rougeau]

Anyway you could walk me through this I've never used MATLAB before this class and the tutorial for what ever reason I can't tie this to anything I did in it.

Answer 2

[Carlos Guerrero García]

Hi Trenton...!!!

You can find my suggestion for an animation plot in

https://es.mathworks.com/matlabcentral/answers/593245-find-the-value-of-the-number-latex-a-a-such-that-the-families-of-curves-latex-y-left-x-c-right