91Ó°ÊÓ

Graph each hyperbola. Label all vertices and sketch all asymptotes. $$ \frac{y^{2}}{36}-\frac{x^{2}}{9}=1 $$

Solve. Remember that graphs can be used to confirm all real solutions. $$\begin{aligned}&y=x^{2}\\\&3 x=y+2\end{aligned}$$

Graph each hyperbola. Label all vertices and sketch all asymptotes. $$ \frac{x^{2}}{25}-\frac{y^{2}}{36}=1 $$

Given: \(x^{2}-y^{2}=4\).Rewrite in standard form. Divide both sides by 4:\\[\frac{x^{2}}{4}-\frac{y^{2}}{4}=1\\],The given is in the standard form of the equation of a hyperbola centered at the origin with horizontal axis:$$\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1$$.where \((-a, 0)\) and \((a, 0)\) are the vertices and \(y=\frac{b}{a} x\) and \(y=-\frac{b}{a} x\) are the asymptotes.where \((-a, 0)\) and \((a, 0)\) are the vertices and \(y=\frac{b}{a} x\) and \(y=-\frac{b}{a} x\) are the asymptotes.From the given, \(a^{2}=4 \Rightarrow a=2\) and \(b^{2}=4 \Rightarrow b=2\) so:VERTICES: (-2,0),(2,0) ASYMPTOTES: \(y=x\) and \(y=-x\),

Solve. Remember that graphs can be used to confirm all real solutions. $$\begin{aligned}&x^{2}-x y+3 y^{2}=27\\\&x-y=2\end{aligned}$$

Solve. Remember that graphs can be used to confirm all real solutions. $$\begin{aligned}&2 y^{2}+x y+x^{2}=7\\\&x-2 y=5\end{aligned}$$

Graph each hyperbola. Label all vertices and sketch all asymptotes. $$ x^{2}-y^{2}=4 $$

Graph each hyperbola. Label all vertices and sketch all asymptotes. $$ 25 x^{2}-16 y^{2}=400 $$

Solve. Remember that graphs can be used to confirm all real solutions. $$\begin{aligned}&x^{2}+4 y^{2}=25\\\&x+2 y=7\end{aligned}$$

Graph each hyperbola. Label all vertices and sketch all asymptotes. $$ 4 y^{2}-9 x^{2}=36 $$$\frac{y^{2}}{b^{2}}-\frac{x^{2}}{a^{2}}=1$