# I have plotted two equations. How to get their intersection point?.......Thanks

2 views (last 30 days)
Maruti Patil on 4 Sep 2015
Commented: Walter Roberson on 9 Sep 2015
ezplot('y-x^2+2.5*x=0');
ezplot('(x-5)^2+(y-3)^2=4');
I have plotted above two equations and I want the exact coordinates of intersection point how to do it?
Walter Roberson on 9 Sep 2015
Are you sure you need the exact coordinates? Because for example one of the x coordinates of the 4 intersections is
x = (1/12) * (3^(1/2) * ((592325 + 720 * 19385^(1/2))^(2/3) + 65 * (592325 + 720 * 19385^(1/2))^(1/3) + 6985)^(3/4) + 15 * (592325 + 720 * 19385^(1/2))^(1/6) * ((592325 + 720 * 19385^(1/2))^(2/3) + 65 * (592325 + 720 * 19385^(1/2))^(1/3) + 6985)^(1/4) - 3^(1/2) * (-((592325 + 720*19385^(1/2))^(2/3) + 65*(592325 + 720*19385^(1/2))^(1/3) + 6985)^(1/2)*(592325 + 720*19385^(1/2))^(2/3) + 130*(592325 + 720*19385^(1/2))^(1/3)*((592325 + 720*19385^(1/2))^(2/3) + 65*(592325 + 720*19385^(1/2))^(1/3) + 6985)^(1/2) + 360*3^(1/2)*(592325 + 720*19385^(1/2))^(1/2)-6985*((592325 + 720*19385^(1/2))^(2/3) + 65*(592325 + 720*19385^(1/2))^(1/3) + 6985)^(1/2))^(1/2))/((592325 + 720*19385^(1/2))^(1/6)*((592325 + 720*19385^(1/2))^(2/3) + 65*(592325 + 720*19385^(1/2))^(1/3) + 6985)^(1/4))
and the corresponding y is at least twice as long.

Doug Hull on 9 Sep 2015
The cheap way to do this is to plot both and zoom in.
ezplot('(x-5)^2+(y-3)^2=4');
hold on
ezplot('y-x^2+2.5*x=0');
This all depends on what you mean by "exact".
The right answer is more along these lines:

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