[kinly]

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.


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.

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.).

b. Investigate the particular case where k = 2, p = 3 and q = 10.

[flyaway]

um well for a, you take the derivative of y
y'=2kx. that's the slope of the tangent lines
2kx=(y-q)/(x-p)
thats the equation. im not sure if that's wat its asking but...um lol i think that should be right

so plug in
b. 2(2)x=(y-10)/(x-3)

wow your problem is worded really weird...like (p,q) usually my teacher just gives us like a x coordinate and asks us for the tangent line equation...well idk if that helped