Find a set of scalar parametric equations for the line formed by the two intersecting planes. 3x+3y+2z+2=0 2x−3y+2z−2=0
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We have the following equation:
If we graph this equation we realize that in fact this is an ellipse with major axis matching the y-axis. So we can recognize these characteristics:
1. Center of the ellipse:
The midpoint C<span> of the line segment joining the foci is called the </span>center<span> of the ellipse. So in this exercise this point is as follows:
</span>
2. Length of major axis:
The line through the foci is called the major axis<span>, so in the figure if you go from -5, at the y-coordinate, and walk through this major axis to the coordinate 1, the distance you run is the length of the major axis, that is:</span>
3. Length of minor axis:
The line perpendicular to the foci through the center is called the minor axis. So in the figure if you go from -2, at the x-coordinate, and walk through this minor axis to the coordinate 2, the distance you run is the length of the minor axis, that is:
4. Foci:
Let's find c as follows:
Then the foci are:
If we graph this equation we realize that in fact this is an ellipse with major axis matching the y-axis. So we can recognize these characteristics:
1. Center of the ellipse:
The midpoint C<span> of the line segment joining the foci is called the </span>center<span> of the ellipse. So in this exercise this point is as follows:
</span>
2. Length of major axis:
The line through the foci is called the major axis<span>, so in the figure if you go from -5, at the y-coordinate, and walk through this major axis to the coordinate 1, the distance you run is the length of the major axis, that is:</span>
3. Length of minor axis:
The line perpendicular to the foci through the center is called the minor axis. So in the figure if you go from -2, at the x-coordinate, and walk through this minor axis to the coordinate 2, the distance you run is the length of the minor axis, that is:
4. Foci:
Let's find c as follows:
Then the foci are: