1. Consider the conic given by the equation 41:2 24: + 9y: + 13;; + 9 = {1. a.) "What kind of oonio is it?I h) Give the coordinates of its vertevaertioes. 1:} Give the coordinates of its foousffooi. 2. Consider the conic given by the equation 41:2 24: + 93; + 13 = . 3.} What kind of conic is it? h} IGi'lire the coordinates of its vertevaertioes. 1:} Give the coordinates of its foousffoei. 3. Find the equation of the hyperbole whose vertioes are at {33}, (3,0) and which goes through the point {3,6}. 4. Find the length of the spiral :r = a\" from a = a to 5- = 2:. . 5. Find the urea. enclosed by the limeqon 1" = 3 + 25in 3. 8.2 Two reversible heat engines operate in series between a source at 527"C and a sink at 17"C. If the engines have equal efficiencies and the first rejects 400 kJ to the second, calculate: (a) the temperature at which heat is supplied to the second engine; (b) the heat taken from the source; (c) the work done by each engine. Assume that each engine operates on the Carnot cycle. 117 8.3 In a Carnot cycle operating between 307 and 17'C the maximum and minimum pressures are 62.4 bar and 1.04 bar. Calculate the cycle efficiency and the work ratio. Assume air to be the working fluid. 8.4 A closed-cycle gas turbine unit operating with maximum and minimum temperatures of 760 and 20"C has a pressure ratio of 7/1. Calculate the ideal cycle efficiency and the work ratio. 8.5 In an air standard Otto cycle the maximum and minimum temperatures are 1400 and 15"C. The heat supplied per kg of air is 800 kJ. Calculate the compression ratio and the cycle efficiency. Calculate also the ratio of maximum to minimum pressures in the cycle. 8.6 A four-cylinder petrol engine has a swept volume of 2000 cm , and the clearance volume in each cylinder is 60 cm . Calculate the air standard cycle efficiency. If the introduction conditions are 1 bar and 24 C, and the maximum cycle temperature is 1400"C, calculate the mean effective pressure based on the air standard cycle. 8.7 Calculate the cycle efficiency and mean effective pressure of an air standard diesel cycle with a compression ratio of 15/1, and maximum and minimum cycle temperatures of 1650"C and 15"C respectively. The maximum cycle pressure is 45 bar. 8.8 In a dual-combustion cycle the maximum temperature is 2000*C and the maximum pressure is 70 bar. Calculate the cycle efficiency and the