Question 62658: find the equation of the set of all points equidistant from the x axis and (4,0).
Answer by jai_kos(139)   (Show Source):
You can put this solution on YOUR website! Given a point (4 ,0) and
Equation along the "x" axis, i.e. y = 0
Distance between a point (x ,y) and the point ( 4 ,0) is given by
sqrt [ ( 0 -x) ^ 2 + ( 4 - y) ^2 ] = equal to the equation of line
sqrt [ ( 0 -x) ^ 2 + ( 4 - y) ^2 ] = y
Square on both sides of the baove equation, we get
[x ^ 2 + ( 4 -y) ^2] = y ^ 2
Simplifying the above step we get,
x^2 + 16 + y ^2 - 8y = y^2
x ^ 2 -8y + 16 = 0
The above equation represent the set of all points equidistant from x -axis and
point ( 4, 0).
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