1) A building has an entry with the shape of a parabolic arch 66 feet high and 46 feet wide at the base. Find an equation for the parabola if the vertex is placed at the origin of the coordinate system.
2) A comet follows the hyperbolic path described by x2/5 - y2/22 = 1, where x and y are in millions of miles. If the sun is the focus of the path, how close to the sun is the vertex of the path?
3) A picture frame has a perimeter of 106 cm and a diagonal √1549 cm. What are the dimensions?
4) Find the vertices of the ellipse: 3x2 + 5y2 - 42x + 40y + 212 = 0
5) A cross-section of an irrigation canal is a parabola. If the surface of the water is 17 feet wide and the canal is 2 feet deep at the center, how deep is it 1 feet from the edge?