<p>Hi this is a problem for my AP Calculus class that i just can't figure out. Any help would or tips would be greatly appreciated. </p>
<p>a. Given a point (p, q) and a parabola y = kx2, find all points on the parabola whose tangents pass through the point. You must consider all possible situations for the location of (p, q) and show your work entirely in the variables k, p and q. </p>
<p>Are there any points for which no tangent exists? If so, describe them both algebraically, in
terms of k, p and q, and also geometrically. Similarly, describe when other situations occur
(one point, two points, etc.). </p>
<p>b. Investigate the particular case where k = 2, p = 3 and q = 10.</p>