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Question 162322: Classify the conic section of each equation.
10. 25x^2 - 9y^2 = 144
I think this may be a circle? But im not for sure and I would love to see the correct steps to finding the answer, i know to rewrite x as x-0 and y as y-0, and i know that 144 is also 12^2,but im not sure where to begin. Thank you!
Found 2 solutions by Alan3354, Fombitz:
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! Classify the conic section of each equation.
10. 25x^2 - 9y^2 = 144
I think this may be a circle? But im not for sure and I would love to see the correct steps to finding the answer, i know to rewrite x as x-0 and y as y-0, and i know that 144 is also 12^2,but im not sure where to begin. Thank you!
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If it were a plus sign, it would be an ellipse. A circle is a special case of the ellipse, and the coefficients of the x^2 and y^2 terms would be the same.
The minus sign makes it a hyperbola.
Answer by Fombitz(32388)  (Show Source):
You can put this solution on YOUR website! Three things to check in conic sections: degree of x and y, coefficient and signs of coefficients.
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Circle : Degree 2 for both x and y, equal coefficients, both positive.
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Parabola : Degree 2 for y and degree 1 for y, coefficients not important.
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Ellipse: Degree 2 for both x and y, unequal coefficients, both positive.
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Hyperbola : Degree 2 for both x and y, coefficients not important, one positive, one negative.
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x and y degree 2.
Coefficients:One positive, one negative.
Hyperbola.
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You could also divide by 144 and look for general forms of conic sections.
The general form for a hyperbola is,
In your case,
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