Determine the conic section given by each of the following equations. Be sure to show all work to find the standard form of the equation of each conic section. 10 points each. Correct conic section (2 points) All work shown (8 points)

1. 3x 2 + 5y 2 12x + 30y = 42

2. x 2 + 3y 2 + 4x = 5

3. x 2 + 2x + 4y = 7

4. 9x 2 + 25y 2 54x 50y 281 = 0

5. 12x 2 4y 2 72x 16y + 44 = 0

Graph each pair of parametric equations. (2 points each)

1. x = 3 sin³t y = 3 cos³t

2. x = 7 sin t + sin 7t y = 7 cos t + cos 7t

2. x = 2t y = t + 5, -2 t 3

2. x = 2t - 1 y = t²+ 5, -4 t 4

2. x = 6 sin t y = 6 cos t, 0 t 2