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.
![219_img1.png](https://secure.tutorsglobe.com/CMSImages/219_img1.png)
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?
![81_img2.png](https://secure.tutorsglobe.com/CMSImages/81_img2.png)
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?