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In questions 1 through 6, explain what these are.

1.  \(3x^2 + 3y^2 = 12\)

a.  An ellipse centered at (0,0) with x-intercepts x = 3, x = -3, and y-intercepts y = 1, y = -1.

b.  A hyperbola with asymptotes y = x, and y = -x

c.  A circle of radius 2 centered at (0, 0)

d.  A circle centered at (-1, 1)

e.  A hyperbola with asymptotes x = 0 and y = 0

2.  \(x^2 + 9y^2 = 9\)

a.  An ellipse centered at (0,0) with x-intercepts x = 3, x = -3, and y-intercepts y = 1, y = -1.

b.  A hyperbola with asymptotes y = x, and y = -x

c.  A circle of radius 2 centered at (0, 0)

d.  A circle centered at (-1, 1)

e.  A hyperbola with asymptotes x = 0 and y = 0

3.  \((x+1)^2 + (y-1)^2 = 1\)

a.  An ellipse centered at (0,0) with x-intercepts x = 3, x = -3, and y-intercepts y = 1, y = -1.

b.  A hyperbola with asymptotes y = x, and y = -x

c.  A circle of radius 2 centered at (0, 0)

d.  A circle centered at (-1, 1)

e.  A hyperbola with asymptotes x = 0 and y = 0

4.  \(y^2 - x^2 = 1\)

a.  An ellipse centered at (0,0) with x-intercepts x = 3, x = -3, and y-intercepts y = 1, y = -1.

b.  A hyperbola with asymptotes y = x, and y = -x

c.  A circle of radius 2 centered at (0, 0)

d.  A circle centered at (-1, 1)

e.  A hyperbola with asymptotes x = 0 and y = 0

5.  \(xy = 1\)

a.  An ellipse centered at (0,0) with x-intercepts x = 3, x = -3, and y-intercepts y = 1, y = -1.

b.  A hyperbola with asymptotes y = x, and y = -x

c.  A circle of radius 2 centered at (0, 0)

d.  A circle centered at (-1, 1)

e.  A hyperbola with asymptotes x = 0 and y = 0

6.  \(x^2 + 2x + y^2 - 2y + 1 = 0\)

a.  An ellipse centered at (0,0) with x-intercepts x = 3, x = -3, and y-intercepts y = 1, y = -1.

b.  A hyperbola with asymptotes y = x, and y = -x

c.  A circle of radius 2 centered at (0, 0)

d.  A circle centered at (-1, 1)

e.  A hyperbola with asymptotes x = 0 and y = 0

In the following two problems, convert from polar coordinates to cartesian coordinates.

7.  \((3, \frac{\pi}{6})\)

a.  \((2, 1)\)

b.  \((\frac{3\sqrt{3}}{2}, \frac{3}{2})\)

c.  \((\frac{3}{2}, \frac{3\sqrt{3}}{2})\)

d.  \((3, 0)\)

e.  \((0, 3)\)

8.  \(r = 5\)

a.  \((3, 4)\)

b.  \(x = 3\)

c.  \(y = 4\)

d.  \(x^2 + y^2 = 5\)

e.  \(x^2 + y^2 = 25\)