Analytic Geometry Answers

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

Find the transformation of the eqn 12x^2-2y^2+z^2=2xy if the origin is kept fixed and the axes are rotated in such a way that the direction ratio of the new axes are (1,-3,0);3,1,0;0,0,1

A positive triangle lake with a side length of 10m, each side should be planted with trees. Question: If the distance between the two trees is ≤ 5m, what's the MINIMUM number of trees needed?

Calculate the area of a triangle whose vertices are given by (3, −1, 2), (1, −1, 2) and (4, −2, 1)