Let L be the line of intersection of the planes cx + y + z = c and x - cy + cz = -1, where c is a real number.
(a) Find symmetric equations for L.
(b) As the number c varies, the line L sweeps out a surface S. Find an equation for the curve of intersection of S with the horizontal plane z = t (the trace of S in the plane z = t)/
The symmetric equations are:
I cannot for the life of me figure out how to get part b.
(a) Find symmetric equations for L.
(b) As the number c varies, the line L sweeps out a surface S. Find an equation for the curve of intersection of S with the horizontal plane z = t (the trace of S in the plane z = t)/
The symmetric equations are:
[FONT=MathJax_Math](x[/FONT][FONT=MathJax_Main]+[/FONT][FONT=MathJax_Main]1[/FONT][FONT=MathJax_Main])/(−[/FONT][FONT=MathJax_Main]2[/FONT][FONT=MathJax_Math]c)[/FONT][FONT=MathJax_Main]=[/FONT][FONT=MathJax_Math](y[/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Math]c/)/[/FONT][FONT=MathJax_Math](c^[/FONT][FONT=MathJax_Main]2[/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Main]1)[/FONT][FONT=MathJax_Main]=[/FONT][FONT=MathJax_Math](z[/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Math]c)/[/FONT][FONT=MathJax_Math](c^[/FONT][FONT=MathJax_Main]2[/FONT][FONT=MathJax_Main]+[/FONT][FONT=MathJax_Main]1)[/FONT]
I cannot for the life of me figure out how to get part b.
Last edited: