I only need answer for #1 and #3,,, thankyouuu

E 4G 9:12 s . . 83 Math102_Problem Set 5... Q . . . FAMILY NAME, FIRST NAME MI. COURSE/YEAR PROBLEM SET 5: Hyperbola DUE ON: May 17, 2021 INSTRUCTIONS: Answer the following items. Show your solutions neatly and completely. MULTIPLE ERASURES ARE NOT ALLOWED. Be organized in writing your answer. Your hyperbola illustration must be PRESENTABLE. 1. Given the following properties of a hyperbola, sketch the graph. State the complete properties: type of hyperbola, center, foci, vertices, endpoints of the conjugate axis, a units, b units, c units, Determine the standard and general equation. [5 points each] a. foci (-3. -7)and (-3. 3), the sum of the distances of any point from the foci is 4. b. center (-3, 5), vertices at (-3, 0) and (-3, 10), one focus at (-3. -3) 2. Given the following equations of a hyperbola, sketch the graph. State the complete properties: type of hyperbola, center. foci, vertices, endpoints of the conjugate axis, a units. b units, c units. a. 144 -=1 109 [4points] b. [5 points ] c. 3x2 - 2yz - 42x - 16y + 67 = 0 [6 points ] 3. A viewing spot tower has a shape of a hyperboloid and is 32 meters high. The rooftop and ground floor are 10 meters in diameter and are symmetric with respect to the middle height of the tower. The circular portion between the rooftop and the ceiling has a diameter of 8 meters. Find the diameter of the circular portion of the viewing spot 20 meters above the ground. [5 points] 4. An explosion is heard by two stations 1600 m apart, located at Fi(-800, 0) and Fa(800, 0). If the explosion was heard in Fi two seconds before it was heard in Fa, identify the possible locations of the explosion. Use 360 m/s as the speed of sound. Suppose that the explosion is due south of station A. how far is the explosion from the station A? [5 points]