Examples for Locus of Points – Key without Sketches
Examples for Locus of Points – Key without Sketches
Describe the locus of points that satisfy each set of conditions. Describe algebraically with an equation those that are starred. (Some may not have meaning is all three settings.)
| |1 Dimension |2 Dimensions |3 Dimensions (Space) |
|Condition |(on a Line) |(on a Plane) |Be prepared to model it. |
| |Draw the figure. |Draw the figure. | |
|3 units from the origin* |Two points |x2 + y2 = 9 |x2 + y2 + z2 = 9 |
| |A(3) and B(-3) | | |
| | |circle with center at the origin and |sphere with center at the origin and |
| | |with radius 3 |with radius 3 |
|Equidistant from two points P and Q* |From P(2) and Q(8) |From P(2,0) and Q(8,0) |From P(2,0,0) and Q(8,0,0) |
| | | | |
| |midpoint at |line which is the perpendicular |plane which is perpendicular to the x |
| |M(5) |bisector of [pic] |axis at (5, 0, 0) |
| | | | |
| | |line x = 5 |plane x = 5 |
|5 units away from x = 2* |two points A(-3) and B(7) |Two lines with equations x = -3 and x |Two planes with equations x = -3 and |
| | |= 7 |x = 7 |
|Equidistant from x = 3 and x = 6* |Point M(4.5) |Line x = 4.5 |Plane perpendicular to the x axis at |
| | | |(4.5, 0, 0) |
| | | | |
| | | |x = 4.5 |
|Equidistant from x = 0 and y = 0* |No meaning |Two lines which bisect the vertical |Two planes which bisect the dihedral |
| | |angles formed by the x and y axes. |vertical angles formed by the planes x |
| | | |= 0 and y = 0 |
| | |Lines y = x and y = -x |Planes y = x and y = -x |
|Equidistant from x = 2 and y = 4* |No meaning |Two lines passing through (2, 4) with |Two planes bisecting the dihedral |
| | |slope 1 and with slope -1 |vertical angles formed by the planes x |
| | | |= 2 and y = 4 |
| | |y = x + 2 and | |
| | |y = -x + 6 |y = x + 2 and |
| | | |y = -x + 6 |
|x2 + y2 = 36 |No meaning |Circle with |Baseless cylinder with axis of the |
| | |center at the origin and radius 6 |cylinder being the z-axis and radius of|
| | | |6 |
|2 units from |No meaning |Two circles with center at the origin |Two baseless cylinders with axis of the|
|x2 + y2 = 36 | |and radii of 4 and 8 |cylinders being the z-axis and radii of|
| | | |4 and 8 |
|6 units from |No meaning |Point at the origin and circle with |The z-axis and baseless cylinder with |
|x2 + y2 = 36 | |center at the origin and radius 12 |axis the z-axis and radius 12 |
|8 units from |No meaning |Circle with center at the origin and |Baseless cylinder with axis being the |
|x2 + y2 = 36 | |radius 14 |z-axis and radius 14 |
|equidistant from |No meaning |Circle with center at the origin and |Baseless cylinder with axis being the |
|x2 + y2 = 4 and | |radius 4 |z-axis and radius 4 |
|x2 + y2 = 36 | | | |
|5 units from the x-axis |No meaning |Lines y = 5 and y = -5 |Baseless cylinder with axis being the |
| | | |x-axis and radius 5 |
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