Read the statements carefully and answer the questions as directed.Problem 1:A satellite dish is shaped like a paraboloid. If the dish is 2 meters wide and 0.5 meters deep, find the equation of the parabola representing the shape of the dish.*4 pointsy^2 = 4xx^2 = 2yy = x^2/4x^2 = 4yProblem 2:An artist wants to create a fountain with a circular pool. If the pool has a radius of 6 feet, what is the equation of the circle representing the pool?*4 pointsx^2 + y^2 = 6x^2 + y^2 = 36x^2 - y^2 = 36y = √(36-x^2)Problem 3:A company designs a water slide in the shape of a hyperbola. The distance between the vertices is 10 meters, and the distance between the foci is 8 meters. Find the equation of the hyperbola.*4 pointsx^2/25 - y^2/16 = 1y^2/25 - x^2/16 = 1x^2/16 - y^2/25 = 1y^2/16 - x^2/25 = 1Problem 4:A cylindrical tank has an elliptical base with semi-major and semi-minor axes of lengths 8 feet and 5 feet, respectively. Write the equation of the ellipse representing the tank's base.*4 pointsx^2/64 + y^2/25 = 1x^2/25 + y^2/64 = 1x^2 + y^2 = 64x^2/16 + y^2/9 = 1

1. Circle A is shown on the coordinate plane shown below.a) Write the center and the radius of the circle.b) Write the equation of the circle.c) Name three points that lie on the circle.d) Find the area of circle to the nearest square unit.    2. Explain the steps necessary to find the center and radius of the circle below.x2 + 4x + y2 ‒ 6y = 9Then, find the center and the radius of this circle and sketch the graph of the circle.   3. Coach Stevens needs to purchase sprinklers to water the baseball field. The standard distance between bases is 90 feet and the infield is a perfect square.Coach Stevens found one sprinkler that sprays a maximum distance of 50 feet. If Coach Stevens placed the sprinkler on the pitcher's mound, would the water spray so that the entire infield was watered? Justify your response.

1. The equation 2x^2+3y^2 = 12 represents which conic section?*4 pointsa) Circleb) Ellipsec) Parabolad) Hyperbola2.  For the equation (x−4)^2​/16 + y^2/9 ​= 1, identify the type of conic section.*4 pointsa) Circleb) Ellipsec) Parabolad) Hyperbola3.  The equation y^2 = 16x represents which type of conic section?*4 pointsa) Circleb) Ellipsec) Parabolad) Hyperbola4.  For the hyperbola (x+2)^2​/ 9  − y^2/4 ​= 1, what are the coordinates of the center?*4 pointsa) (-2, 0)b) (2, 0)c) (0, -2)d) (0, 2)5.  The equation x^2−6x+9+y^2 = 0 represents which conic section?*4 pointsa) Circleb) Ellipsec) Parabolad) Hyperbola

A water fountain is designed to shoot a stream of water in the shape of a parabolic arc. The equation of the parabola is given by ℎ(𝑡)=−0.5𝑡2+4𝑡+1h(t)=−0.5t 2 +4t+1, where ℎ(𝑡)h(t) represents the height of the water stream in meters and t  represents the time in seconds since the water was shot. Answer the following questions.Determine the maximum height reached (in meters).

Instructions: Use the given information to answer the questions and interpret key features. Use any method of graphing or solving.  Round to one decimal place, if necessary.An irrigation system (sprinkler) has a parabolic pattern. The height, in feet, of the spray of water is given by the equation h(x)=−x2+10x+7.5ℎ(𝑥)=−𝑥2+10𝑥+7.5, where x𝑥 is the number of feet away from the sprinkler head (along the ground) the spray is.The irrigation system is positioned Answer 1 Question 6 feet above the ground to start.The spray reaches a Answer 2 Question 6 height of Answer 3 Question 6 feet at a horizontal distance of Answer 4 Question 6 feet away from the sprinkler head.The spray reaches all the way to the ground at about Answer 5 Question 6 feet away.

Sunita had a hemispherical bowl of radius 𝑟.She made a conical vessel of radius 𝑟 with a tinsheet.(i) find the height of the conical vessel so that it canhold the water same as that of the hemisphericalbowl.(ii) If the radius of the cone formed in the above part is 14 cm, then find how much sheet isused?(iii) If the height of the conical vessel is doubled, how much more water can it hold than thehemispherical bowl?