Expert: Richard J. Raridon - 5/21/2004

Question
1. find all points of intersection of the circle x^2 + y^2 =9 and the hyperbola x^2/4 - y^2 =1
2. find xy in the equation:
   xy=1073
   (x+3)(y-7)=960
3. one earthquake monitoring station determines that the center of a quake is 30miles away. A second station 40 miles east and 10 miles north of the first finds that it is 20 miles from the quake's center.
a. supppose the first station is at the origin of a coordinate system. Write a system of equations to describe this situation.
b. solve the system and find the coordinates of all possible locations of the quake's center.
4. the shape of the light beam from a flashlight is a cone. when that cone of light hits a flat surface, the outline is a conic section. Tell whcih conic section is formed when the flashlight is held in the following manner.
a. at an angle of about 75 degreee to the wall.
5. a skydiver jumping from a plane falls about 16ft the first second, 48ft the next second, and 80ft. the third second. the sequence of distances is aritmetic if air resistance is ignored. How many feet will the diver fall in the 13th second?

Answer
1. x = +/- 2(2)^1/2, y = +/- 1
2. x = 29, y = 37 and x = -15.86, y = -67.67
3. a. x^2+y^2 = 30^2 and (x-40)^2 +(y-10)^2 = 20^2
b. x = 22.56, y = 19.78 is one solution
4. I suspect it's an ellipse
5. The sequence is not arithmetic since the distance is not linear with time.  
The distance fallen as a function of time = 16t^2
and the time for any given second = 16(t2^2 -t1^2)
so for the 13th second, the distance = 16(13^2-12^2) = 400ft