Use MATLAB software to find the following Please include all

Use MATLAB software to find the following. Please include all programming codes used.

Find all the points where the curves (below) intersect: [ (x+1)^2 / 4 ] + [ (y-1)^2 / 9 ] = 1 AND y = e^(x)

i) First, plot these two curves using equal scales to see how many points of intersection there are, and approximately where they are.

ii) Then use fzero to calculate each point

Solution

S = solve(eqn,var)
S = solve(eqn,var,Name,Value)
Y = solve(eqns,vars)
Y = solve(eqns,vars,Name,Value)
[y1,...,yN] = solve(eqns,vars)
[y1,...,yN] = solve(eqns,vars,Name,Value)
[y1,...,yN,parameters,conditions] = solve(eqns,vars,\'ReturnConditions\',true)
Description

S = solve(eqn,var) solves the equation eqn for the variable var. If you do not specify var, the symvar function determines the variable to solve for. For , solve(x + 1 == 2, x) solves the equation x + 1 = 2 for x.

S = solve(eqn,var,Name,Value) uses additional options specified by one or more Name,Value pair arguments.

Y = solve(eqns,vars) solves the system of equations eqns for the variables vars and returns a structure that contains the solutions. If you do not specify vars, solve uses symvar to find the variables to solve for. In this case, the number of variables that symvar finds is equal to the number of equations eqns.

Y = solve(eqns,vars,Name,Value) uses additional options specified by one or more Name,Value pair arguments.

[y1,...,yN] = solve(eqns,vars) solves the system of equations eqns for the variables vars. The solutions are assigned to the variables y1,...,yN. If you do not specify the variables, solve uses symvar to find the variables to solve for. In this case, the number of variables that symvar finds is equal to the number of output arguments N.
[y1,...,yN] = solve(eqns,vars,Name,Value) uses additional options specified by one or more Name,Value pair arguments.

[y1,...,yN,parameters,conditions] = solve(eqns,vars,\'ReturnConditions\',true) returns the additional arguments parameters and conditions that specify the parameters in the solution and the conditions on the solution.

x = fzero(fun,x0) tries to find a zero of fun near x0, if x0 is a scalar. fun is a function handle. See Function Handles in the MATLAB Programming documentation for more information. The value x returned by fzero is near a point where fun changes sign, or NaN if the search fails. In this case, the search terminates when the search interval is expanded until an Inf, NaN, or complex value is found.

Parameterizing Functions Called by Function Functions, in the MATLAB mathematics documentation, explains how to provide additional parameters to the function fun, if necessary.

If x0 is a vector of length two, fzero assumes x0 is an interval where the sign of fun(x0(1)) differs from the sign of fun(x0(2)). An error occurs if this is not true. Calling fzero with such an interval guarantees fzero will return a value near a point where fun changes sign.

x = fzero(fun,x0,options) minimizes with the optimization parameters specified in the structure options. You can define these parameters using the optimset function. fzero uses these options structure fields:

[ (x+1)^2 / 4 ] + [ (y-1)^2 / 9 ] = 1
y=e^(x)

syms x y
equ1 = [(x+1)^2 / 4 ] + [ (y-1)^2 / 9 ] = 1;
equ2 = y=e^(x)
S = solve([equ1,equ2], [x, y])
S.x
S.y
ezplot(equ1,[S.x,S.y]);
fun = @(x) myfun(equ1,S.x);
x = fzero(fun,0.1)