Apply the revised contents on Analytical Geometry.

Question 1 A programmer carried out a simulation of a car accident, when the accident occurs three bodies will be left in different parts of the road, he observes that in his simulation the coordinates that he will assign to the bodies will be the origin and the centers of the circumferences.

x^2+12x+y^2-2ky-37+k^2=0

x^2-6x+y^2+4y+12=0

Find the value of k that the programmer needs if he knows that the bodies form a triangle whose area is 4.

Question 2 Find the value of x necessary for the point P(x, 3) to be equidistant from the points A(3, -2) and B(7, 4)

Question 3 Find the length of the median of side AB of the triangle whose vertices are A(-2, -2), B(6, 0), and C(2,8). (The median is the line that joins the midpoint of one side of the triangle with the opposite vertex.) x_medium = (x_A + x_B) / 2 = (-2 + 6) / 2 = 4 / 2 = 2 y_medium = (y_A + y_B) / 2 = (-2 + 0) / 2 = -2 / 2 = -1 Therefore, the midpoint of AB is M(2, -1). Calculate the length of the median

Question 4

The arch of a window in a computer lab is parabolic in shape. The height of the arch at the midpoint is 16 feet and the width at the base is 7 feet. If you want to pass a box that has several CPUs, this box will be slid through the window. If the box is 12 feet tall, what is the maximum possible width that the box can be?

Question 5

a) Consider the following conics:

2x^2+2y^2+3x+5y5=0

Determine what conic it is, its elements, and graph.

b) Find the reduced equation of the ellipse that verifies:

I. passes through (25, 0) and the semifocal distance is 7.

II. passes through (4, 1) and through (0, 3).

thanks