Rotate the axes so that the new equation contains no xy-term. Discuss the new equation.17x2 - 12xy + 8y2 - 68x + 24y -12 = 0
A. ? = 63.4°
x'2 = -16y'
parabola
vertex at (0, 0)
focus at (0, -4)
B. ? = 63.4°
+ 
= 1
ellipse
center at (
, - 
)
major axis is x'-axis
vertices at (4 + 
, - 
) and (-4 + 
, - 
)
C. ? = 26.6°
+ 
= 1
ellipse
center at (0, 0)
major axis is y'-axis
vertices at (0, ±4)
D. ? = 63.4°
- 
= 1
hyperbola
center at (0, 0)
transverse axis is the x'-axis
vertices at (±4, 0)
Answer: B
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A. vertex (-1, 1)
intercept (0, 2)
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intercepts (0, 0), (-2, 0)
C. vertex (1, 1)
intercept (0, 2)
D. vertex (1, -1)
intercepts (0, 0), (2, 0)
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A. independent: t; dependent, r B. independent: r; dependent, t
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