## 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). 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>```