You can create paraboloids using the quadric object.
Here's a mirror as it is used in a Newton reflector-telescope:

#default {
	pigment { color rgb <1,1,1> }
	finish { ambient 0.5 diffuse 0.5 }
}

#declare focal_length = 10;
#declare ms = 1/4/focal_length;
#declare mainMirror = difference {
	cylinder { <0.01,0,0>,<-ms,0,0>,1 }
	quadric {
		<0,1,1>,<0,0,0>,<1,0,0>,0
		scale <ms,1,1>
		finish { ambient 0 diffuse 0 reflection 1 }
	}
}


plane { y,-2 pigment { checker } }
light_source { <-100,100,0> color rgb <1,1,1> }
camera { location <-3,1,-3> look_at <0,0,0> }

object { mainMirror }

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