Question

How do you graph x^2- 3y^2=-11?

Answer 1

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

Answer 2

Like a hyperbola.

Answer 3

Divide by -11
\[ -\frac{x^{2}}{11} -(\frac{-3}{11})y^{2} = 1 \rightarrow \frac{y^{2}}{\frac{11}{3}} - \frac{x^{2}}{11} =1\]

Answer 4

center: (0,0)
\[a^{2} = \frac{11}{3}\rightarrow a = \sqrt{\frac{11}{3}}\]
\[b^{2} = 11 \rightarrow b = \sqrt{11}\]
vertices: (0, +-a)
\[c^{2} = a^{2} +b^{2} = \frac{11}{3}+11 = \frac{44}{3}\]
\[c = \sqrt{\frac{44}{3}}\]
foci: (0, +-c)

Answer 5

were you able to finish the graph?................
do you have to do the slant asymptotes also?