Question

Find an equation for the surface consisting of all points p for which the distance from p to the y-axis is half the distance from p to the xz-plane. sketch or briefly describe the surface

Answer 1

Let P (x,y,z) be the point in xyz plane such that the distance from p to the y axis is twice the distance from p to the xz- plane i.e,

If d1= 2d2 ………………..(1)

But D1=√X²+Z²

d2=y

substitute d1and d2 in (1), we have

√x²+z²= 2y

X²+y²-4y²=0