(x^2)/9 + (y^2)/16 + z^2 = 1 i) Sketch the traces in the three coordinate planes

Question

(x^2)/9 + (y^2)/16 + z^2 = 1

i) Sketch the traces in the three coordinate planes. Label points of intersection on axis.
ii) Sketch the traces in at least one plane parallel to each of the coordinate planes.
iii) Sketch the surface is R^3. Label points of intersection on the axis.

Explanation / Answer

i)In xy plane: z = 0 =>x^2/3^2 + y^2/4^2 = 1 =>it is an ellipse with major axis 4 and minor axis of 3 In xz plane: y = 0 =>x^2/3^2 + z^2/1^2 = 1 =>it is an ellipse with major axis 3 and minor axis of 1 In zy plane: x = 0 =>y^2/4^2 + z^2/1^2 = 1 =>it is an ellipse with major axis 4 and minor axis of 1

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