Script to find an intersection of two surfaces and a tangent line

This is a script that I use in class to validate and visualize the results of a 2 step problem which asks students to find a parametric equation representing the intersection of two surfaces:  z=x^2+3y^2 and x=y^2 and then to find the tangent line to this curve at the point (1,1,4).

parametric-intersection

screen shot of the script

Feel free to copy this script into a text file and save as .txt file for future use or editing.  To learn more about using scripts, please see the Scripting with CalcPlot3D user guide.

<init steps="5">
<step 1>
 <window>
 xmin ="-4"
 xmax ="4"
 xscale ="1"
 ymin ="-4"
 ymax ="4"
 yscale ="1"
 zmin ="-1"
 zmax ="10"
 zscale ="1"
 zMinClip ="-4"
 zMaxClip ="8"
 centerXPercent ="0.5"
 centerYPercent ="0.5"
 hsrMode ="0"
 rotationSteps ="40.0"
 autoSpin ="true"
 anaglyph ="none"
 edgesOn ="true"
 facesOn ="true"
 opaque ="true"
 transparency ="140"
 smooth ="false"
 antialiasAll ="false"
 showBox ="false"
 showAxes ="true"
 perspective ="true"
 whiteBackground ="false"
 colorBrightness ="0.1"
 gridSize ="25"
 zoom ="0.7"
</window>
<viewPoint center="(8.23639103546332, 4.755282581475766, 3.0901699437494745)"
 focus="(0.0, 0.0, 0.0)"
 up="(0.0, 0.0, 2.0)"/>
<function type ="z = f(x, y)" function = "x^2+3y^2" num ="1" visible = "true" format = "Normal" />
</step>
<step 2>
 <window>
 xmin ="-4"
 xmax ="4"
 xscale ="1"
 ymin ="-4"
 ymax ="4"
 yscale ="1"
 zmin ="-1"
 zmax ="10"
 zscale ="1"
 zMinClip ="-4"
 zMaxClip ="8"
 centerXPercent ="0.5"
 centerYPercent ="0.5"
 hsrMode ="0"
 rotationSteps ="40.0"
 autoSpin ="true"
 anaglyph ="none"
 edgesOn ="true"
 facesOn ="true"
 opaque ="true"
 transparency ="140"
 smooth ="false"
 antialiasAll ="false"
 showBox ="false"
 showAxes ="true"
 perspective ="true"
 whiteBackground ="false"
 colorBrightness ="0.1"
 gridSize ="25"
 zoom ="0.7"
</window>
<viewPoint center="(8.23639103546332, 4.755282581475766, 3.0901699437494745)"
 focus="(0.0, 0.0, 0.0)"
 up="(0.0, 0.0, 2.0)"/>
<function type ="x = f(y, z)" function = "y^2" num ="2" visible = "true" format = "Normal" />
</step>
<step 3>
 <window>
 xmin ="-4"
 xmax ="4"
 xscale ="1"
 ymin ="-4"
 ymax ="4"
 yscale ="1"
 zmin ="-1"
 zmax ="10"
 zscale ="1"
 zMinClip ="-4"
 zMaxClip ="8"
 centerXPercent ="0.5"
 centerYPercent ="0.5"
 hsrMode ="0"
 rotationSteps ="40.0"
 autoSpin ="true"
 anaglyph ="none"
 edgesOn ="true"
 facesOn ="true"
 opaque ="true"
 transparency ="140"
 smooth ="false"
 antialiasAll ="false"
 showBox ="false"
 showAxes ="true"
 perspective ="true"
 whiteBackground ="false"
 colorBrightness ="0.1"
 gridSize ="25"
 zoom ="0.7"
</window>
<viewPoint center="(8.23639103546332, 4.755282581475766, 3.0901699437494745)"
 focus="(0.0, 0.0, 0.0)"
 up="(0.0, 0.0, 2.0)"/>
<function type ="z = f(x, y)" function = "x^2+3y^2" num ="1" visible = "true" format = "Normal" />
 <function type ="x = f(y, z)" function = "y^2" num ="2" visible = "true" format = "Reversed Color" />
</step>
<step 4>
 <window>
 xmin ="-4"
 xmax ="4"
 xscale ="1"
 ymin ="-4"
 ymax ="4"
 yscale ="1"
 zmin ="-1"
 zmax ="10"
 zscale ="1"
 zMinClip ="-4"
 zMaxClip ="8"
 centerXPercent ="0.5"
 centerYPercent ="0.5"
 hsrMode ="0"
 rotationSteps ="40.0"
 autoSpin ="true"
 anaglyph ="none"
 edgesOn ="true"
 facesOn ="true"
 opaque ="false"
 transparency ="140"
 smooth ="false"
 antialiasAll ="false"
 showBox ="false"
 showAxes ="true"
 perspective ="true"
 whiteBackground ="false"
 colorBrightness ="0.1"
 gridSize ="25"
 zoom ="0.7"
</window>
<viewPoint center="(8.23639103546332, 4.755282581475766, 3.0901699437494745)"
 focus="(0.0, 0.0, 0.0)"
 up="(0.0, 0.0, 2.0)"/>
<function type ="z = f(x, y)" function = "x^2+3y^2" num ="1" visible = "true" format = "Normal" />
 <function type ="x = f(y, z)" function = "y^2" num ="2" visible = "true" format = "Reversed Color" />
</step>
<step 5>
 <window>
 xmin ="-4"
 xmax ="4"
 xscale ="1"
 ymin ="-4"
 ymax ="4"
 yscale ="1"
 zmin ="-1"
 zmax ="10"
 zscale ="1"
 zMinClip ="-4"
 zMaxClip ="8"
 centerXPercent ="0.5"
 centerYPercent ="0.5"
 hsrMode ="0"
 rotationSteps ="40.0"
 autoSpin ="true"
 anaglyph ="none"
 edgesOn ="true"
 facesOn ="true"
 opaque ="false"
 transparency ="140"
 smooth ="false"
 antialiasAll ="false"
 showBox ="false"
 showAxes ="true"
 perspective ="true"
 whiteBackground ="false"
 colorBrightness ="0.1"
 gridSize ="25"
 zoom ="0.7"
</window>
<viewPoint center="(8.236391035463319, 4.755282581475766, 3.0901699437494745)"
 focus="(0.0, 0.0, 0.0)"
 up="(0.0, 0.0, 2.0)"/>
<function type ="z = f(x, y)" function = "x^2+3y^2" num ="1" visible = "true" format = "Normal" />
 <function type ="x = f(y, z)" function = "y^2" num ="2" visible = "true" format = "Reversed Color" />
 <curve>
 x = "t^2"
 y = "t"
 z = "t^4+3t^2"
 tMin = "-2"
 tMax = "2"
 tSteps = "100"
 tValue = "0"
 showPt = "true"
 ptSize = "9"
 trace = "true"
 arrowSize = "18.0"
 velocity = "false"
 acceleration = "false"
 showTrace = "false"
 view2D = "false"
 width = "4"
 showArrows = "false"
 numArrows = "8"
 transformArrows = "false"
 color = "255, 0, 0"
 colorMode = "PLAIN"
 showTNB = "false"
 showTNBEqs = "false"
 showTNBLabels = "false"
 showOscPlane = "false"
 showRectPlane = "false"
 showNormPlane = "false"
 TNBScale = "1.0"
 showOscCircle = "false"
 showCurvature = "false"
 </curve>
</step>
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