Conic Sections - Hyperbolas

$$y^2-\frac{x^2}{4}=1$$

Find the center:

$$\frac{\left(x-1\right)^2}{4}-\frac{\left(y+2\right)^2}{1}=1$$

Find the vertices:

$$\frac{\left(x-1\right)^2}{4}-\frac{\left(y+2\right)^2}{1}=1$$

$$\frac{\left(x-1\right)^2}{4}-\frac{\left(y+2\right)^2}{1}=1$$

a=​ (a)  

b=​ (b)  

c=​ (c)  

in hyperbolas, true or false: $$c^2=a^2-b^2$$ ​ (d)  

Find the equation of the hyperbola:

$$x^2-9y^2+2x-54y-161=0$$

$$\frac{\left(x+1\right)^2}{81}-\frac{\left(y+3\right)^2}{9}=1$$

Find the equation of the specified hyperbola with its center at the origin:

Vertices: $$\left(0,\pm2\right)$$

Foci: $$\left(0,\pm4\right)$$

Find the equation of the specified hyperbola with its center at the origin:

Vertices: $$\left(0,\pm8\right)$$

Asymptotes: $$y=\pm4x$$

Find an equation of the specified hyperbola.

Vertices: $$\left(4,1\right)\ and\ \left(4,9\right)$$

Foci: $$\left(4,0\right)\ and\ \left(4,10\right)$$

Find an equation of the specified hyperbola:

Vertices: $$\left(2,0\right)\ and\ \left(6,0\right)$$

Foci: $$\left(0,0\right)\ and\ \left(8,0\right)$$