78 Find equations of the traces in the coordinate planes andsketch the traces in an

Chapter 11, Problem 8

(choose chapter or problem)

Find equations of the traces in the coordinate planes and sketch the traces in an \(xyz\) - coordinate system. [Suggestion: If you have trouble sketching a trace directly in three dimensions, start with a sketch in two dimensions by placing the coordinate plane in the plane of the paper, then transfer the sketch to three dimensions.]

(a) \(y^{2}+9 z^{2}=x\)

(b) \(4 x^{2}-y^{2}+4 z^{2}=4\)

(c) \(z^{2}=x^{2}+\frac{z^{2}}{4}\)        

Equation Transcription:

Text Transcription:

xyz

y^2 + 9z^2 = x

4x^2 - y^2 + 4z^2 = 4

z^2 = x^2 + frac{z^2}{4}