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# Circle in 3d space.

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Let S be the graph of x2 +z2 +6z=16 in 3d-space.

(a) The intersection of S with the xz-plane is a circle with center____ and radius_____
(b) The intersection of S with the xy-plane is two lines, x=_____ andx=_____
(c) The intersection of S with the yz-plane is two lines, z =_____    and z =_____

Guest Mar 2, 2017

#2
+26412
+10

Also note that the equation can be rewritten as follows

$$x^2+z^2+6z=16 \\ \rightarrow x^2+z^2+6z+3^2=16+3^2 \\ \rightarrow x^2+(z+3)^2=25 \\ \rightarrow (x-0)^2+(z-(-3))^2=5^2$$

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Alan  Mar 2, 2017
Sort:

#1
+26412
+10

This 3d graph should help:

.

Alan  Mar 2, 2017
#2
+26412
+10

Also note that the equation can be rewritten as follows

$$x^2+z^2+6z=16 \\ \rightarrow x^2+z^2+6z+3^2=16+3^2 \\ \rightarrow x^2+(z+3)^2=25 \\ \rightarrow (x-0)^2+(z-(-3))^2=5^2$$

.

Alan  Mar 2, 2017

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