Hi I need help solving the following problems with complete solution

the topic is about conic section: Ellipse

1. The ceiling in the hallway 10 m wide is in the shape of a semiellipse and is 9 m high in the center and 6 m high at the side walls. Find the height of the ceiling 2m from either wall. 2. Suppose that the orbit of a planet is in the shape of an ellipse with major axis whose length is 500 million km. If the distance between the foci is 400 million km, find an equation of the orbit. 3. An arch is in the form of a semiellipse. It is 48 ft wide at the base and has a height of 20ft. How wide is the arch at a height of 10 ft above the base? 4. The orbit of the earth around the sun is elliptical in shape with the sun at one focus and semimajor axis of length 185.8 million miles. If the distance of the sun from the center of the orbit is 1.58 million miles, find a. the greatest distance from the sun to Earth, and b. the least distance from the sun to Earth