Which equation describes a circle?

A: -2y2+y+2x2-5x-3=0

B: -3x2+x-6y2+y=4

C: -3y2+x+y=3

Identify the conic section with the given equation 5x2-6y2-9x+2y+3=0

p.s. the twos are supposed to be raised to that power

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- Jul 8th 2006, 07:01 PMLane2 math questions:p
Which equation describes a circle?

A: -2y2+y+2x2-5x-3=0

B: -3x2+x-6y2+y=4

C: -3y2+x+y=3

Identify the conic section with the given equation 5x2-6y2-9x+2y+3=0

p.s. the twos are supposed to be raised to that power - Jul 8th 2006, 10:33 PMrgep
None of those is a circle. In a general quadratic form, if the coefficients of x^2 and y^2 are equal, it's a circle; unequal but the same sign, an ellipse; one zero and one non-zero, a parabola; of different sign, a hyperbola (rectagular if the coefficients are equal in absolute value). So you have a rectangular hyperbola, an ellipse and a parabola respectively.

- Jul 8th 2006, 10:46 PMearbothQuote:

Originally Posted by**Lane**

as rgep explained this equation describes a hyperbola.

Greetings

EB - Jul 9th 2006, 05:27 AMThePerfectHacker
The quadradic in form of,

$\displaystyle

ax^2+2hxy+by^2+2gx+2fy+c=0$

can de determined by looking a the relationship between,

$\displaystyle h^2$ and $\displaystyle ab$.

$\displaystyle h^2=ab$---->parabola

$\displaystyle h^2>ab$---->hyperbola

$\displaystyle h^2<ab$---->ellipse

In your case we have #2 which is a hyperbola.

[Note: Some cases where not considered such as the coditions for a general quadradic to represent a line or to represent a point]