Rotate the axes so that the new equation contains no xy-term. Discuss the new equation.x2 + xy + y2 - 3y - 6 = 0

A. ? = 45°
 +  = 1
ellipse
center at (0, 0)
major axis is y'-axis
vertices at (0, ±2)
B. ? = 45°
 +  = 1
ellipse
center at (, )
major axis is y'-axis
vertices at (, - ) and (, )
C. ? = 45°
y'2 = -18x'
parabola
vertex at (0, 0)
focus at (- , 0)
D. ? = 45°
 -  = 1
hyperbola
center at (0, 0)
transverse axis is the x'-axis
vertices at (±, 0)

Answer: B

Mathematics

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