Question

classify the conic section and write its equation in standard form:
#1- 9x^2+49y^2+392y+343=0

#2- x^2+y^2+4y-5=0

Answer 1

If you have the signs in front of x^2 and y^2 have different signs, then most likely you have a hyperbola
it's standard form is
\[\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1 \text{ or } \frac{(y-k)^2}{b^2}-\frac{(x-h)^2}{a^2}=1 \]
If you have the same sign but the coefficients are not equal (still talking about x^2 and y^2), then most likely you have an ellipse
it's standard form is
\[\frac{(x-h)^2}{a^2}+\frac{(y-k)^2 }{b^2}=1 \]
if the coefficients are the same (still talking about x^2 and y^2), then most likely it is a circle
it's standard form is
\[(x-h)^2+(y-k)^2=r^2 \]
Now a parabola, one of the coefficients of x^2 or y^2 will be 0 (but not both)
and it's standard form is
\[(x-h)^2=4p(y-k) \text{ or } (y-k)^2=4p(x-h) \]

Answer 2

so out of what I just say, your equations are most likely what?

Answer 3

the answer choices for #1 are
A.) hyperbola
(y-1)^2/4-x^2/25=1
B.) ellipse
x^2/49+(y+4)^2/9=1
C.) ellipse
x^2/9+(y+4)^2/49=1
D.)parabola
x=-2y^2=3

Answer 4

ok and I'm asking you to look at what I said and tell what kinda graph it is most likely to give us

Answer 5

Oh, sorry I thought you were asking me what my equations were, read that wrong sorry.
Okay so would it be a...hyperbola? because the signs in front of y^2 and x^2 are different..

Answer 6

so that - thing in front of your equation is part of your problem?
like it is a negative sign or just the way they are numbered
1-
2-

Answer 7

that's just the way they are numbered
1-
2- and then the equation

Answer 8

so that would mean the x^2 and y^2 coefficients are both same in sign then

Answer 9

so definitely not a hyperbola

Answer 10

hyperbola you would have different signs

Answer 11

oh I thought you meant how ones 9x^2 and ones 49y^2, so then would it be a ellipse right?