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a surface consists of all point P such that the distance from P to the plane y = 1 is twice the distance from P to the point Q(0,-1,0). Find the equation for this surface and identify it.

Solution:

the plane y = 1 is all point (x,y,z) such that y = 1.. So can i label an arbitrary point on the y plane (x,1,z)?

I will label the point (x,1,z) Point G

and i will assign the ordered triple (x

_{0},y

_{0},z

_{0}) to Point P

If that step if valid I then came up with the following equation....

|PG|

^{2}= (2|GQ|)^2.

Next I proceeded to solve for x

_{0},y

_{0},z

_{0}for LHS which should give me the equation of the surface...

Is this correct?

I hope my explanation to my solution is understandable