Question 975243: ) Classify each of the following graphs (parabola, circle, ellipse, hyperbola):
a) 3x2 + 3y2 – 6x – 2 = 0
b) 3x2 + 4y2 + 2x + 1 = 0
c) 3x2 – 5y2 – 12x + 15y – 18 = 0
d) 3x2 + 6x – 4y + 12 = 0
e) 3x2 + 6x – 3y2 – 12y + 7 = 0
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Classify each of the following graphs (parabola, circle, ellipse, hyperbola):
a) 3x2 + 3y2 – 6x – 2 = 0
x^2 and y^2 have equal coefficients:: circle
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b) 3x2 + 4y2 + 2x + 1 = 0
x^2 and y^2 have unequal coefficients:: ellipse
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c) 3x2 – 5y2 – 12x + 15y – 18 = 0
x^2 and y^2 have coefficients with opposite signs:: hyperbola
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d) 3x2 + 6x – 4y + 12 = 0
Only x is squared:: parabola
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e) 3x2 + 6x – 3y2 – 12y + 7 = 0
3(x^2 + 2x + 1) - 3(y^2 + 4y + 4) = -7+3-12
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Since the right side is negative, not a conic
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Cheers,
Stan H.
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