Question

x^2 -3y^2 +8y =0
is that a hyperbola, ellipse or what? whats that in general form

Answer 1

Hyperbola!

Answer 2

hmm

Answer 3

It is a hyperbola not a circle :)

Answer 4

r is here radius...

Answer 5

\[x^2 -3y^2 +8y=x^2 -3(y^2 -\frac{8}{3}y+\frac{16}{9}-\frac{16}{9})=x^2 -3(y^2 -\frac{8}{3}y+\frac{16}{9})+\frac{16}{3}=0\\ x^2 -3(y -\frac{4}{3})^2=-\frac{16}{3} \\ 3(y -\frac{4}{3})^2-x^2=\frac{16}{3}\]

A hyperbola

Answer 6

Equation of a hyperbola
\[\frac{(y-h)^2}{a^2}-\frac{(x-k)^2}{b^2}=1\]