3 algebra questions!

all info in screenshots below. I will need this in pdf form if you have any questions just let me know! 🙂

15. The equation of a parabola is 12y = (x-1)2 – 48. Identify the vertex, focus, and directrix of the (4 points)
parabola.
16. Skip designs tracks for amusement park rides. For a new design, the track will be elliptical. If (3 points)
the ellipse is placed on a large coordinate grid with its center at (0,0), the equation
x2 12
1 models the path of the track. The units are given in yards. How long is the
2500 8100
major axis of the track? Explain how you found the distance.
+
17. A hyperbolic mirror can be used to take panoramic photos, if the camera is pointed toward the (3 points)
mirror with the lens at one focus of the hyperbola. Write the equation of the hyperbola that can
be used to model a mirror that has a vertex 4 inches from the center of the hyperbola and a
focus 1 inch in front of the surface of the mirror. Assume the mirror has a horizontal transverse
axis and the hyperbola is centered at (0,0).