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A focal chord of $y^2=4ax$ makes an angle $\theta$ with the axis of the parabola. How do I find the length of the chord?

I tried using the parametric equation but couldn't go further.

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Some hints:

  • What are the coordinates of the focus of the parabola?
  • What is the equation of the line that makes an angle $\theta$ with the $y$-axis and goes through the focus? (This line contains the focal chord given in the question.)
  • At what two points does this line intersect the parabola?
  • Finally, what is the distance between these two points?
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