Question

1. Produce traces of the surface parallel to the three standard axes then the use traces to sketch the surface. x² = 4,² +2² a b. y = 2r? +2? z + x2 = 5

Answer 1

x² = 4y² + Z² "Z trace O- 4y'tz'=0 >> y Leo xy trace Zeo =) x²= 4y parabola in xu plane pour of lines. ZX trace y = 0 x²= z² y= 2x²4 z' YZ racace uz plane 2-0 ~ y= z² parabola in > 42 1. Z-0 xy trace & y= 2x² ZX trace 7-Z-0 y=0 > 2x+z²= = Z+x=s. x²5 - 7=415 pairs of llel lines 7-0 =) =) x4 trace Z-5 =) O-k YZ trace - ) plane x ²5-2 z=5-1² - parabola in az plane. Zx toace y = 0

x? = x2 + 4 y2 Geometric figure: infinite elliptic cone Surface plot: 5 -5 -2 -5 0 5

plot y=+*+2 x Geometric figure: elliptic paraboloid 3D plot: 1.0-1.0 -0.5 0.0 2 0.5 0.0 0.5 1.0 -0.5 -1.0, 31 1

plot Z+= 5 Implicit plot: 10 X -4 -2 2 4 -5