Question

X^2+y^2=2(2y-x+2)
How do I tell this equation is a parabola, circle, ellipse, or hyperbola without graphing?

Answer 1

look to see if the coefficients on the \(x^2\) and \(y^2\) terms are equal or not

Answer 2

you don't even have to multiply on the right or collect like terms or anything to see it

Answer 3

So I only have to see if x^2 and y^2 and equal for it to be a circle?

Answer 4

maybe i was not clear
the "coefficients" have to be equal \[2x^2+3y^2+\text{stuff}=\text{whatever}\] is an ellipse

Answer 5

\[2x^2-3y^2+\text{stuff}=\text{whatever}\] is a hyperbola

Answer 6

Circles are going to be in the form ax^2+by^2+cx+dx+e

Where a b c d e are any real number

Answer 7

\[x^2+y^2+\text{stuff}=\text{whatever}\] is a circle as is \[3x^2+3y^2+\text{stuff}=\text{whatever}\] because the coefficients are the same

Answer 8

@sunnnystrong actually no, for a circle the coefficients for the square terms must be equal

Answer 9

Thanks

Answer 10

Okay a b c d e are any real number but the squaredterms must be equal. Exucse im using openstudy mobile and its terrible