Graphing a hyperbola with tangent lines

Hello,

I keep attempting to graph a function of a hyperbola, which is coming out okay.

The issue I am having is that I want to inclue two tangent lines on this hyperbola. I have the x values of each of the tangent lines, but I do not know how to make matlab find the y values for the given x, and then plot them.

Here is my function :

syms x y;

F(x,y) = 2*y-3*x-3*x*y+x^2+y^2-6;

Also I am using fimplicit to plot this hyperbola initially. Is this correct? Can anyone offer insight on how to graph these tangent lines? Ive attempted so many methods in the last 2 days and they all come close, but the tangent lines arent exactly "Tangent looking" For example one or the other lies directly on the curve.

My given x value is 8.9

Answer 1

[darova]

I just exstracted data from ezplot handle

syms x y
F = 2*y-3*x-3*x*y+x^2+y^2-6;
h = ezplot(F,[-1 1]*10);
x1 = get(h(1),'xdata');
x2 = get(h(2),'xdata');
y1 = get(h(1),'ydata');
y2 = get(h(2),'ydata');

hold on
plot([x1(1) x2(1)],[y1(1) y2(1)])
plot([x1(end) x2(end)],[y1(end) y2(end)])
hold off

achievement