Find intersection of curve and line.

i have two equations yw and y1 i need to find intersection of both line and curve and then find the distance of the point from origin. i have only points of y and x for making the curve and have used polynomial interpolation for that

clear

syms x1

x=[0;1;2;3];

y=[7;5;11;28];

for i=1:4

for j=1:4

a(i,j)=power(x(i),(j-1));

end

end

b=inv(a)*(y);

yw=tan(deg2rad(10))*x1+20;

y1=b(1,1)+(b(2,1)*x1)+(b(3,1)*x1.^2)+(b(4,1)*x1.^3);

fplot(yw,[0,5])

hold onclc

fplot(y1,[0,5])

Answer 1

[Star Strider]

Try this:

syms x1
x=[0;1;2;3];
y=[7;5;11;28];
for i=1:4
    for j=1:4
        a(i,j)=power(x(i),(j-1));
    end
end
b=inv(a)*(y);
yw=tan(deg2rad(10))*x1+20;
y1=b(1,1)+(b(2,1)*x1)+(b(3,1)*x1.^2)+(b(4,1)*x1.^3);

xv = vpasolve(y1-yw==0,x1)                                  % X-Value At Intersection
yv = subs(yw, x1, xv)                                       % Y-Value At Intersection

figure
fplot(yw,[0,5])
hold on
fplot(y1,[0,5])
plot(double(xv), double(yv), '+r')
hold off
xlim([0 5])
legend('yw','y1','Intersection', 'Location','best')

.

[A Akhilesh]

Hey!, thanks for the answer. i would like to know if the same thing would work when i have n points defining my curve, which gives me an nth degree polynomial.

[Star Strider]

As always, my pleasure!

Calculating the intersections of lines defined by data (rather than expressions) from two different data sets is similar in concept, although the code differs. See Plot a point of intersection between 2 lines or curves for a typical approach.