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Mathematics
Problem
The locus of a point which moves in such a way that its distance from the line
x
1
=
y
1
=
z
−
1
\frac{x}{1} = \frac{y}{1} = \frac{z}{-1}
1
x
=
1
y
=
−
1
z
is twice the distance from the plane
x
+
y
+
z
=
0
x + y + z = 0
x
+
y
+
z
=
0
is a.
x
2
+
y
2
+
z
2
−
5
x
−
3
y
−
3
z
=
0
x^2 + y^2 + z^2 - 5x - 3y - 3z = 0
x
2
+
y
2
+
z
2
−
5
x
−
3
y
−
3
z
=
0
b.
x
2
+
y
2
+
z
2
+
5
x
+
3
y
+
3
z
=
0
x^2 + y^2 + z^2 + 5x + 3y + 3z = 0
x
2
+
y
2
+
z
2
+
5
x
+
3
y
+
3
z
=
0
c.
x
2
+
y
2
+
z
2
−
5
x
y
−
3
y
z
−
3
z
x
=
0
x^2 + y^2 + z^2 - 5xy - 3yz - 3zx = 0
x
2
+
y
2
+
z
2
−
5
x
y
−
3
y
z
−
3
z
x
=
0
d.
x
2
+
y
2
+
z
2
+
5
x
y
+
3
y
z
+
3
z
x
=
0
x^2 + y^2 + z^2 + 5xy + 3yz + 3zx = 0
x
2
+
y
2
+
z
2
+
5
x
y
+
3
y
z
+
3
z
x
=
0
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