Precalculus B: Conic Sections Hyperbola Test 2.0

Write in standard hyperbolic form, $$x^2-4y^2+10x+32y-75=0$$ :

What is the value of a² for the given hyperbola?

What are the equations of the asymptotes of the hyperbola in the picture?

Find the equation of the hyperbola.

What is the center of the hyperbola?

$$\frac{y^2}{9}-(x+4)^2=1$$

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

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

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

Asymptotes: $$y=\pm4x$$