I need help on these problems tutors. Thank you!

Write an equation for the ellipse. Type the left side of the equation in the box below. 1=1Find the equation of the parabola described. Find the two points that define the latus rectum, and graph the equation. Vertex at (0,0); axis of symmetry the y-axis; containing the point (5,6) .. . What is the equation of the parabola? (Use integers or fractions for any numbers in the equation.) Find the two points that define the latus rectum. The left point is and the right point is (Type ordered pairs. Simplify your answers.) Use the graphing tool to graph the equation. Click to enlarge graphFind an equation for the ellipse. Graph the equation. foci at ( 1 3,0); y-intercepts are 1 6 Type the left side of the equation of the ellipse. =1A hall 180 feet in length is to be designed as a whispering gallery. If the foci are located 40 feet from the center, how high will the ceiling be at the center? The ceiling will be about |feet high. (Type an integer or decimal rounded to one decimal place as needed.)Suppose that two people standing 2 miles apart both see the burst from a fireworks display. After a period of time, the first person standing at point A hears the burst. Four seconds later, the second person standing at point B hears the burst. If the person at point B is due west of the person at point A and if the display is known to occur due north of the person at point A, where did the fireworks display occur? Note that sound travels at 1100 feet per second. The fireworks display is feet north of the person at point A. (Do not round until the final answer. Then round to the nearest foot as needed.)