Question 162322
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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{{{25x^2 - 9y^2 = 144}}}
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.
{{{25x^2/144-9y^2/144=1}}}
The general form for a hyperbola is,
{{{(x-h)^2/a^2-(y-k)^2/b^2=1}}}
In your case,
{{{h=0}}}
{{{k=0}}}
{{{a^2=(144/25)}}}
{{{a=12/5}}}
{{{b^2=(144/9)}}}
{{{b=12/3}}}