Coordinate type problem help
Dave is going to leave academia and go into business building grain silos. A grain silo is a cylinder with a hemispherical top, used to store grain for farm animals. Here is a 3D view, a cross-section, and the top view.
If Dave is standing next to a silo of cross-sectional radius r = 8
feet at the indicated position, his vision will be partially obstructed. Find the portion of the y-axis that Dave cannot see. (Hint: Let a be the x-coordinate of the point where line of sight #1 is tangent to the silo; compute the slope of the line using two points (the tangent point and (12, 0)). On the other hand, compute the slope of line of sight #1 by noting it is perpendicular to a radial line through the tangency point. Set these two calculations of the slope equal and solve for a. Enter your answer using interval notation. Round your answer to three decimal places.)
I have been stuck on this problem, any help on how to approach it? Thank you!
Re: Coordinate type problem help
cylinder is represented by a central circle with radius r=8. Write down the equation of that circle. Next find the equations for tangents passing through the point (12,0). You only need one of two tangents since you have symmetry about the abscissa. So if you can calculate the equation of one tangent line passing through the point (12,0) you can easily answer the question. If b is the point of intersection of one tangent line and y-axis then the portion that Dave cannot see is [-b,b]