Analytic Geometry Answers

Find an equation of the sphere that has center (2,3,-1) and contains the point (1,7,-9)

Find an equation of the sphere that has radius 1 and center in the first octant and is tangent to each coordinate plane

Find an equation of the sphere that has endpoints of a diameter at A and B

A(1,4,-2) B(-7,1,2)

Find an equation of the sphere with center c that is tangent to (a) the xy-plane, (b) the xz- plane and (c) the yz-plane

(i)C(-2,4,-6)

Find an equation of the sphere with center c that is tangent to (a) the xy-plane, (b) the xz- plane and (c) the yz-plane

(i)C(-2,4,-6)

Find the vector that has (a) the same direction as A and twice the magnitude of A, (b) the opposite direction of a and one-third the magnitude of a, and (c) the same direction as A and magnitude 2.

(i)A=14i-15j+6k

Determine the equation of the plane containing the points P(1,3,2) Q=(-2,0,-2) and R=(1,4,3)

Find the parametric equations for the line L through P(5,-2,4) that is parallel to (1/2, 2, -2/3)

(i) where does line L intersect the xy- plane?

(ii) sketch the position vector for a and the line L.

1.Discuss the graph of the equation x^2 +y^2 + z^2 -6x +8y+4z+4=0

1. Find the midpoint of the segment with ends (4, -3, 1) and (-2, 5, 3).

2. Determine whether the vectors u=3i+j-2k and v=2i-4j+k are orthogonal.

3. Describe and sketch 9x^2 + 9y^2 - 4z^2=0