The equation is:
3x^2-20y^2=80y+48
I know it is a hyperbola once I check with Wolfram Alpha. But, I need a definite way of knowing it is.
I tried setting it up in the standard form by trying to isolate 48.
3x^2-20y^2-80y=48
Then divide by 48 to make the right side equal 1 like the standard form for it is.
3x^2/48-(20y^2-80y)/48=1
But that is still not its standard form because I don't know what y^2 is... how can I get it to be just y^2?
"How can I determine this is a parabola?"
first note that tonio shows how to derive 'standard' form. Wilmer had shown'general form'.
full conic general form is
a quick way to determine if you have parabola,hyperbola or ellipse is to look at A and C terms.
if there is only one second power term you have a parabola.
if C is negative you have a hyperbola.
if A and C are positive you have ellipse.
in standard form just look at the sign in between the terms '-'=hyperbola '+'=ellipse
to determine algebraically with NO B term.
A=C circle
AC > 0 = ellipse
AC = 0 = parabola
AC < 0 = hyperbola
to determine algebraically with B term use the discriminate.
discriminate < 0 = ellipse
discriminate = 0 = parabola
discriminate > 0 = hyperbola
Hello, thyrgle
Answer: no.Is this a parabola? .
Skoker explained the equation of the general conic equation,
. . which includes conics which have been "rotated".
If there is no xy-term, the conic is "horizontal" or "vertical".
. . Its axis is parallel to a coordinate axis.
Then the equation can be "eyeballed" to identify the conic.
The general equation of this conic is: .
We are concerned with and only, the coefficients of and
If or (but not both), we have a parabola
If , we have a circle.
If and have the same sign: ellipse.
If have opposite signs: hyperbola.
Note: the above forms include degenerate and imaginary conics.
For example: . is a degenerate circle.
And: . is an imaginary ellipse.