For the collection of all locations that are equally spaced apart from (0,0,2) and the xy plane, find an equation.

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Brittany Patton · Accepted Answer

The given point and the plane P(0,0,2) and xy pane  It asks to find an equation for the set of all point. whereas, the distance between this equation and the point equal the distance between the same equation and xy-plane (xy-plane means z = 0). Use the distance formula (x−0)2+(y−0)2+(z−2)2=(x−x)2+(y−y)2+(z−0)2  Square both sides of an equation x2+y2+(z−2)2=0+0+z2  Solve x2+y2+(z−2)2=z2  x2+y2+z2−4z+4=z2  x2+y2−4z+4=0  The required equation z=x24+y24+1

Vasquez · Accepted Answer

Answer:The equation for the collection of all locations that are equally spaced apart from (0, 0, 2) and the xy plane is given by z=2 and z=−2.Explanation:The distance between the point (x, y, z) and the xy plane can be determined using the formula for the distance between a point and a plane. The equation of the xy plane is given by z = 0.The formula for the distance between a point (x, y, z) and the plane Ax + By + Cz + D = 0 is:Distance=|Ax+By+Cz+D|A2+B2+C2In our case, the equation of the plane is z = 0, which can be rewritten as 0x + 0y + 1z - 0 = 0. By comparing this equation with the general form Ax + By + Cz + D = 0, we can see that A = 0, B = 0, C = 1, and D = 0.Plugging these values into the formula, we get:Distance=|0x+0y+1z−0|02+02+12=|z|1Since we want the distance to be equal to the distance between the point (0, 0, 2) and the xy plane, we can set the distance as 2. Therefore, we have:|z|1=2To remove the absolute value, we can consider two cases:Case 1: z ≥ 0In this case, the equation becomes:z1=2⟹z=2Case 2: z &amp;lt; 0In this case, the equation becomes:−z1=2⟹−z=2⟹z=−2Therefore, the collection of all locations that are equally spaced apart from (0, 0, 2) and the xy plane can be represented by the equations:z=2z=−2

RizerMix · Accepted Answer

The equation of the collection of all locations that are equally spaced apart from (0,0,2) and the xy plane is:(x−0)2+(y−0)2+(z−2)2=r2 where r is the radius of the collection of locations.

Don Sumner · Accepted Answer

Step 1: Let&#039;s consider a point in the collection, which can be represented as (x, y, z). The distance between this point and the point (0, 0, 2) can be calculated using the distance formula:d=(x−0)2+(y−0)2+(z−2)2Since the points in the collection are equally spaced apart from (0, 0, 2) and the xy-plane, the distance between any point and the xy-plane can be considered as a constant value. Let&#039;s denote this constant distance as &#039;c&#039;.Step 2: Thus, we have the equation:x2+y2+(z−2)2=cSquaring both sides of the equation to eliminate the square root, we get:x2+y2+(z−2)2=c2This equation represents the collection of all locations that are equally spaced apart from (0, 0, 2) and the xy-plane.

Find an equation for the set of all points equidistant

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