Consider the graph of 2- 4y 2 0. What does the cross-section in the ry-plane loo
ID: 2884038 • Letter: C
Question
Consider the graph of 2- 4y 2 0. What does the cross-section in the ry-plane look like? A. a hyperbola B. a circle C. a point D. a parabola E. an ellipse F. empty G. a line or lines 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. parabolas C. hyperbolas D. circles What does the cross-section in the plane look like? A. a circle B. empty C. a hyperbola D. a parabola E. an ellipse F. a point G. a line or lines 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. parabolas B. hyperbolas C. ellipses D. circlesExplanation / Answer
X2-4Y+Z2=0
In XY plane, Z=0 . Thus the equation becomes X2-4Y=0 which is a parabola.
A plane Parallel to XY plane will be Z=a ( where a is a constant ). THen the equation becomes X2-4Y+constant=0 which is again a parabola
In YZ plane, X=0, which implies the equaion becomes -4Y + Z2= 0This is a parabola.
A plane Parallel to YZ plane will be X=a ( where a is a constant ). THen the equation becomes Z2-4Y+constant=0 which is again a parabola
In XZ plane, Y=0, which implies the equaion becomes X2 + Z2= 0This is a point ( origin ).
A plane Parallel to XZ plane will be Y=a ( where a is a constant ). THen the equation becomes X2+ Z2 =constantwhich is a circle