Math 445 Assignment 5A (due FRIDAY 1/31)

5-1 Intersecting a certain line with a sphere

Let N = (0,0,1) and let the plane F be the (x,y,0) plane (i.e., the z = 0 plane).

• For any point Q = (a, b, 0) in F, write the points of line NQ in parametric form. (i.e., in terms of an affine parameter t).

• Let E be the sphere with center (0,0,0) and radius 1.  Write the equation in x, y, z that defines this sphere.

• By substituting the points on NQ into the equation for E, solve for t and find the points of intersection of NQ with E.  The answers will be in terms of a and b.