Find an equation for the set of all points equidistant from the planes y = 3 and y = -1.

1 Answers

Best Answer

The given two planes
y=3, y=-1
it s to find an equation for the set of all point. whereas, the distance between this equation and the first plane equal the distance between the same equation and the second plane... (Use the distance formula)
sqrt((x-x)^(2)+(y-(-1))^(2)+(z-z)^(2))=
sqrt((x-x)^(2)+(y-3)^(2)+(z-z)^(2))
square both sides of an equation
sqrt(0+(y+1)^(2)+0)=sqrt(0+(y-3)^(2)+0)
solve
(y+1)^(2)=(y-3)^(2)
y^(2)+2y+1=y^(2)-6y+9
8y=8 -> y=1
Result:
y=1