Analytic Geometry Answers

Find the vertex, focus, and Directrix of each parabola.
1. (x+2)^2=20(y+5)
2. (y-1)^2=-16(x+4)
3. (x-5)^2=4(y+1)
4.(y-3)^2=12(x+1)
5. (x+4)^2=6(y-5)

An archeologist found the remains of an ancient wheel, which she then placed on a grid. If an arc of the wheel passes through A(–7, 0), B(–3, 4) and C(7, 0), locate the center of the wheel, and the standard equation of the circle defining its boundary.

Find the vector equation of the line passing through 2i - 3j and i + j + k. Which point on this line has direction cosines, 1/√3, 1/√3, 1/√3 and why?

find the standard equation of the circle C(3,-2) ; r=4

Find the equation of the cylinder whose base is the circle x^2 + y^2 = 4, z = 0 and the axis is x= y/2 = z.

Give the equations of three planes that meet in three lines.

Three planes can intersect in a number of different ways. For each of the combinations below, find the single point of intersection if there is one. If there isn't, explain how the planes do intersect.
a. 3x+4y+2z-1=0 -2x + 5y + 3z + 7 = 0 5x + 4y + 2z − 3 = 0
b. x−2y+3z−1=0 -3x + 5y + 2z + 7 = 0 -x + y + 8z + 5 = 0

The coordinates of points A and B are A (16,4) and B (34,40). What are the coordinates of a point that partitions segment AB in a ratio of 1:5?

Check whether the surface represented by
x^2 + y^2 = 2 (z + 1) is symmetric about the YZ-plane, ZX-plane and XY-plane. Do the coordinate axes intersect the surface?

Find the equation of the sphere which pass through the circle x^2+y^2+z^2=9,2x+2y-7=0& the touch the plane x-y+z+3=3