General Instructions:" 1. Use permanent black or blue-inked permanent pen. 2. Answer in a long-sized paper. 3. Label well the components of your test. 4. Academic Integrity! Do not allow others to diminish the value of your honest efforts and achievements. Best of luck! 1. Classify the graph of the equation as circle, a point, an empty set, a parabola, an ellipse, a hyperbola, or lines. Show your proof. . Box your final answer. (35 pts) 1. 4x2 - 8x - 49y2 + 196y - 388 = 0 2. x2 + 5x + y2- y+7=0 3. 49x2 + 196x + 100y2 + 1400y + 196 = 0 36x2 + 360x + 64y2 - 512y + 1924 = 0 5. x2+y2 - 18y - 19=0 6. y2 - 48x + 6y = -729 7. -5x2+ 60x + 7y2 +84y +72=0 11. Answer the problem below. Show your solution to support your answer. Box your final answer. (10 pts) Cross section of a nuclear cooling tower is in the shape of a hyperbola with yz 302 442 = 1. The tower is 150-m tall and the distance from the top of the tower to the center of the hyperbola is half the distance from the base of the tower to the center of the hyperbola. Find the diameter of the top and the base of the tower