Minimum length of projection

Question

Let BC be the latus rectum of the parabola $y^2 =4ax$ with vertex A . Then what is the Minimum length of the projection of BC on a tangent drawn in the portion BAC .

I thought about it a lot but could not get any start .

Could anybody provide me with a hint?

Answer 1

Here's a hint. First, try answering these three questions.

1. What's the equation of the tangent of a parabola?
2. If you have two lines making an angle $\theta$ with each other, how do you find the component or projection of one's length on the other? First consider this in the case of vectors. The same applies here too.
3. How do you find the minimum value of an algebraic expression. Hint: It has something to do with the derivative.

If you managed to answer them, now try applying those in solving this problem.