Consider the graph of r -y 42 0. What does the cross-section in the ry plane loo

Question

Consider the graph of r -y 42 0. What does the cross-section in the ry plane look like? A. a parabola B. a hyperbola C. an ellipse D. a circle E. empty F. a line or lines G. a point What do the cross-sections parallel to the plane look like? (Some of them may be empty--tell me about the ones that aren't) A. hyperbolas B. circles C. parabolas D. ellipses What does the cross-section in the plane look like? A. a point B. an ellipse C. a hyperbola. D. a line or lines E. a parabola F. empty G. a circle What do the cross-sections parallel to the plane look like? (Some of them may be empty--tell me about the ones that aren't.) A. ellipses B. hyperbolas C. parabolas D. circles

Explanation / Answer

X2-Y2-4Z=0

In XY plane, Z=0

Thus the equation becomes: X2-Y2 = 0 => X=+/- Y which is a line or lines. Therefore ans is F

In plane parallel to XY plane, Z= a ( constant )

Thus the equation becomes: X2-Y2 = constant which is a hyperbola. Therefore ans is A

In YZ plane, X=0

Thus the equation becomes: Y2 = 4Z which is a parabola. Therefore ans is E

In a plane parallel to YZ plane, X = Constant

Thus the equation becomes: Y2 - 4Z = constant which is a parabola. Therefore ans is C

In XZ plane, Y=0

Thus the equation becomes: X2 = 4Z which is a parabola. Therefore ans is F

In a plane parallel to XZ plane, Y = Constant

Thus the equation becomes: X2 - 4Z = constant which is a parabola. Therefore ans is C

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