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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?

Ajay Subramanian
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search
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1 Answers1

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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.

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

Community
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Ajay Subramanian
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  • Feel free to ask me for the solution if you're still facing some difficulty:) – Ajay Subramanian Apr 28 '17 at 13:21
  • Which equation of tangent , there can be infinite number of tangent – search Apr 28 '17 at 13:47
  • First, obtain the general equation of a tangent of the parabola in terms of the coordinates of a general point $(x_1,y_1)$. Then, find the slope ($tan\theta$) of the tangent. Now, take the component of the length of the latus rectum on the tangent ($4asin\theta$). Differentiate this expression to get for which the projection is minimum and substitute in the expression. – Ajay Subramanian Apr 28 '17 at 13:56