I. Match each equation to the corresponding conic section:(Rx2) A. Circle B. Parabola C. Ellipse D. Hyperbola

1. 24x2 + 9x - 12y = -4y2 + 102
2. 4y + x2 + 3x = 0

3. 6x2 - 7x + 6y2 = -4y + 3
4. 14x2 - 9y2 = 5x - y + 39
5. 2x2 + 2y2 - 4x + 12y - 18 = 0

II. Solve the following problems. (Rx3)

1. The parabolic cable of a 60m portion of the roadbed of a suspension bridge is positioned as shown below. Vertical Cables are to be spaced every 6m along this portion of the roadbed. Find the standard equation of the parabola.

2. A satellite dish has a shape called a paraboloid, where each cross-section is a parabola. Since radio signals (parallel to the axis) will bounce the surface of the dish to the focus, the receiver should be placed at the focus. How far should the receiver be from the vertex, if the dish is 12 ft across, and 4.5ft deep at the vertex?

3. A Ferris wheel is elevated 1 m above ground. When a car reaches the highest
point on the Ferris wheel, its altitude from ground level is 31 m. How far
away from the center, horizontally, is the car when it is at an altitude of
25 m?

4. A tunnel has the shape of a semi ellipse that is 15 ft high at the center, and 36 ft across at the base. At most how high should a passing truck, if it is 12 ft wide, for it to be able to fit through the tunnel? Round off your answer to two decimal places.

5. Two control towers are located at points Q(500, 0) and R(500, 0), on a straight shore where the x-axis runs through (all distances are in meters). At the same moment, both towers sent a radio signal to a ship out at sea, each traveling at 300 m/µs. The ship received the signal from Q 3 µs (microseconds)before the message from R. Find the equation of the curve containing the possible location of the ship.