Intersection of multivariate graphs

Sanelma shared this question 1 year ago
Answered

Hi, I have two multivariate functions graphed: f(x,y)=x^2 + y^2 and g(x,y) = xy+2. I would like to show the curve of intersection of these two graphs. Is this possible? Couldn't get it to work with regular "intersect" command.

Comments (7)

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The projection of the intersection onto the xOyPlane is:

x² + y² - x y - 2 = 0
Curve(2 / sqrt(2) (sin(t) - cos(t) / sqrt(3)), 2 / sqrt(2) (sin(t) + cos(t) / sqrt(3)), t, 0, 2π)


so the intersection is

Curve(2 / sqrt(2) (sin(t) - cos(t) / sqrt(3)), 2 / sqrt(2) (sin(t) + cos(t) / sqrt(3)),f(2 / sqrt(2) (sin(t) - cos(t) / sqrt(3)), 2 / sqrt(2) (sin(t) + cos(t) / sqrt(3))), t, 0, 2π)
https://www.geogebra.org/m/ebkfuyaj

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Hi Michael,

I'd like to show the curve of the intersection of x^2+4y^2+9z^2=1 and z = h x + c.

Please see the link below.

I also want to an animation point on this intersection curve.

Is it possible?

https://ggbm.at/tpybbn2y

Thank you so much for your help.

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That's easier, there's a command for that :)

IntersectPath( <Plane>, <Quadric> )

Try:

c:IntersectPath(a, b)
A=Point(c)
StartAnimation(A)

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Thank you, Michael!

Actually I have a surface.Is there a command for Intersection of a surface and a plane?

I try yours but it didn't work.

Thank you for your reply.

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Hi Sanelma!


One possibility is to solve the equation f(x,y)=g(x,y) and to use the solution for drawing one rather two curves.


77094456cbed6ba77f7d184cdf587393


Greetings

mire2

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That's very nice!


I think you need an extra +2 on the z-coordinate

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Oh - thank you for your kind words and yes, I forgot the +2 on the z-coordinate, so all must be above the x-y-plane.

Good looks!

Kind regards

mire2

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