# Thread: find parametric equation for curve

1. ## find parametric equation for curve

question:Curve C is the intersection of plane $z=1+y$ and $z=\sqrt{x^2+y^2}$
C is a parabola, a conic section.

Find parametric equations for C

my worklugging z=1+y into first equation I get [tex]1+y=\sqrt{x^2+y^2}[tex]

problem: I don't know what to do next

hint:use t as parameter, with x=t (-infinity<t<infinity)

2. 1 + y = sqrt(x^2 + y^2)

square both sides

1 + 2y + y^2 = x^2 + y^2

y =[ x^2 - 1]/2

x= t

y = [t^2 - 1]/2

z= 1 + y = [t^2 +1]/2