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Question 190691: determine whether the following equations represent a parabola, circle, ellipse or hyperbola
4x^2 + 6y^2 - 4x - 9y + 12 = 0
3x^2 + 2x - 5y + 12 = 0
4x^2 + 4y^2 -4x + 9y + 1 = 0
9x^2 + 12 y^2 + 4x + 4y + 4 = 0
5x^2 - 2y^2 + 2x - 6y - 6 = 0
How do I determine this?
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! determine whether the following equations represent a parabola, circle, ellipse or hyperbola
4x^2 + 6y^2 - 4x - 9y + 12 = 0
A theoretical ellipse. It has x^2 and y^2 terms added with differing coefficients. However, the axes are less than zero. If the last term is -12, then it's an ellipse.
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3x^2 + 2x - 5y + 12 = 0
A parabola. Only x is 2nd degree.
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4x^2 + 4y^2 -4x + 9y + 1 = 0
A circle. x^2 and y^2 with coefficient 4.
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9x^2 + 12 y^2 + 4x + 4y + 4 = 0
A theoretical ellipse. It has x^2 and y^2 terms added with differing coefficients. However, the axes are less than zero. If the last term is -4, then it's an ellipse.
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5x^2 - 2y^2 + 2x - 6y - 6 = 0
A hyperbola. The x^2 and y^2 terms have different signs.
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How do I determine this?
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