Exam 14: Parametric Equations and Conic Sections

$(x-4)^{2}+(y+3)^{2}=16$ is a circle of radius 4 centered at $(-4,3)$

What is the upper focal point of the ellipse $16 x^{2}+4 y^{2}-64 x-24 y+36=0$ ? Where necessary, round to 2 decimal places.

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

Write a parameterization of one branch of the following hyperbola using hyperbolic functions : $3(y+2)^{2}-5(x-4)^{2}=1, y<-2$ .

The parameterization for the right half of the hyperbola $\frac{(x-5)^{2}}{9}-\frac{(y-3)^{2}}{4}=1$ using hyperbolic functions is $x=a+b \cosh t, y=c+d \sinh t,-\infty<t<\infty$ , where a =----------,b =--------,c =------,and d =----------.

Find the center, vertices, and asymptotes for the following hyperbola: $y^{2}-4 x^{2}+8 x=8$

What happens to the graph of the hyperbola $\frac{x^{2}}{n^{2}}-\frac{y^{2}}{n^{2}}=1$ as $n$ decreases?

Does the hyperbola $9 x^{2}-4 y^{2}+54 x-8 y+41=0$ open left-right or up-down?