5. HAND IN Find parametric equations for the set oflines that pass through the point [2, 0. O) and are tangent to the sphere x2 + 3'2 + 22 = 1. Some helpd discussion You've probably never solved a problem like this but. believe it or not, you do have the technical knowledge that it requires. To get some common notation we will called the fixed point P = [2, 0. 0] and let Q be the variable point of tangency on the sphere. Your typical tangent line will have two parameters in it. One is the parameter I that we use to draw lines in 3-space. In this regard. recall that the line passing through two given points P anins P+t(QP) {00 grim} But the point Q will contain another parameter that will index different points at which the line is tangent to the sphere. In working with this second paranleterization, it will be helpful to recall a parametrization of the circle. You hopefully did this in grade 11. The diagram at the right depicts the unit circle cen- tred at the origin. The point on the circle whose ray makes an angle 6 [O E 6' s 360] with the positive x-axis is (c0509). sin(l9]] The point at 6' : 50 is depicted in the diagram. htt s: wx-vwdesmos.com calculator lhkkzZ f u The question you need to ask is what does the set on points look like? The first thing you might do is solve the 2-dimensional analogue: nd parametric equations for the lines that pass through the point [2. 0] and are tangent to the circle 362 + _v2 = 1. If you draw the diagram for this problem. it will give you a nice insight into the 3-space version