Hi everyone,
I have a question about how to create a Manipulate[] that allows changing the point in which the tangent is drawn. It should display the hyperbola, the asymptotes, the tangent the resulting triangle.
the hyperbola of equation is x^2/9-y^2/2=1
I already made the split and the asymptotes and the tangent Here is my code
hb = Solve[x^2/9 - y^2/2 == 1 && x > 0 && y > 0, Reals];
{x0, y0} = {x, y} /. First@hb /. x -> 4;
(*asymptotes formula = (x^2/a^2)-(y^2/b^2)=0*)
(*tangent line at point (x0,y0) --> xx0/a^2-yy0/b^2)=2 *)
contours =
ContourPlot[{x^2/9 - y^2/2 == 1, x^2/9 - y^2/2 == 0,
x*x0/9 - y*y0/2 == 1}, {x, -5, 5}, {y, -5, 5},
Epilog -> {Black, Point[{x0, y0}]}, AspectRatio -> Automatic,
ContourStyle -> {Pink, Orange, Purple}];
region =
ImplicitRegion[{x^2/9 - y^2/2 <= 1, x^2/9 - y^2/2 >= 0,
x*x0/9 - y*y0/2 <= 1}, {{x, 0, 10}, {y, -10, 10}}];
plotreg = RegionPlot[region, PlotStyle -> LightBlue];
Show[contours, plotreg, PlotRange -> All]
![enter image description here](https://community.wolfram.com//c/portal/getImageAttachment?filename=Untitled.png&userId=2686895)