Determine the center of the ellipse \(\frac{(x-1)^2}{4}+\frac{(y-4)^2}{9}=1\)

Write the equation \(4x^2-8x+9y^2-72y+112=0\) in standard form. 

What kind of polar plot is produced by the equation \(r=2+5\cos(\theta)\)? (Hint, you can just plot it)

Determine a unit vector pointing in the direction of \(\langle 3,4\rangle \).

Determine the sum of the vectors \(\mathbf{u}=\langle 3,1\rangle\) and \(\mathbf{v}=\langle 1,3\rangle\)

Convert \((4,2)\) from cartesian coordinates to polar coordinates.

Determine the foci of the ellipse given by the equation \(\frac{x^2}{4}+\frac{y^2}{49}=1\)

Which of these graphs matches the equation \((x-1)^2-\frac{(y-2)^2}{4}=1\).

Convert the equation \(x^2+y^2=4y\) from cartesian to polar coordinates.

Below in the left-side column are a list of “checks” that balance out our branches of government.  Correctly identify the two branches that are associated with that “check” in the right-side column.