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How to draw a hyperbolic paraboloid

The steps. Identify the axisIdentify the parabolasDraw two parabolasDraw two hyperbolasConnect the hyperbolas. Identify the axis. Write equation in the form u, v, and w are x,y, and zu = x, v = y, w = z u = x, v = z, w = yu = y, v = x, w = z u = y, v = z, w = xu = z, v = x, w = y u = z, v = y, w = xThe one of degree 1, u, is the axisIf the equation is, Then u = x, v = y, w = z, a = 1, b = 1axis is the x-axis.

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How to draw a hyperbolic paraboloid

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    1. How to draw a hyperbolic paraboloid

    2. The steps Identify the axis Identify the parabolas Draw two parabolas Draw two hyperbolas Connect the hyperbolas

    3. Identify the axis Write equation in the form u, v, and w are x,y, and z u = x, v = y, w = z u = x, v = z, w = y u = y, v = x, w = z u = y, v = z, w = x u = z, v = x, w = y u = z, v = y, w = x The one of degree 1, u, is the axis If the equation is, Then u = x, v = y, w = z, a = 1, b = 1 axis is the x-axis

    4. Identify the parabolas Two parabolas are used for the sketch The remaining two variables in the equation, v and w, are used for the parabolas the upper parabola the lower parabola For the upper parabola is the lower parabola is

    5. Draw the parabolas The upper parabola is in the uv-plane The lower parabola is in the uw-plane For The upper parabola is in the xy-plane The lower parabola is in the xz-plane Determine reasonable limits for the domain values for the two parabolas Upper: x = y^2; limit y to [-2,2] or [-1,1] Lower: x = -z^2; limit z to [-2,2] or [-1,1]

    6. Draw the parabolas (1/2)

    7. Draw the parabolas (2/2)

    8. Draw the hyperbolas One hyperbola for each of the parabolas Drawn in planes perpendicular to the axis Upper hyperbola drawn with upper parabola The plane is the upper bound for the u variable For this is the plane x = 4 Vertices are on the upper parabola Lower hyperbola drawn with lower parabola The plane is the lower bound for the u variable For this is the plane x = 4 Vertices are on the lower parabola

    9. Draw the hyperbolas (1/2)

    10. Draw the hyperbolas (2/2)

    11. Connect the hyperbolas Connect the upper hyperbola, upper ends, to the lower hyperbola, upper ends Connect the upper hyperbola, lower ends, to the lower hyperbola, lower ends If the two hyperbola arcs are appropriately matched (see the document An Interesting Property of Hyperbolic Paraboloids), then these line segments lie on the surface of the hyperbolic paraboloid.

    12. Connect the hyperbolas (1/2)

    13. Connect the hyperbolas (2/2)

    14. Graph with sketch lines

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