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COMEDK · Maths · 13. Parabola

- The locus of the mid-points of the line joining the focus and point on the parabola \(y^{2}=4 a x\) is a parabola with the equation of directrix as

  1. A \(x+a=0\)
  2. B \(2 x+a=0\)
  3. C \(x=0\)
  4. D \(x=\frac{a}{2}\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(x=0\)

Step-by-step Solution

Detailed explanation

Let the mid-point of any point \(P\left(x_{1}, y_{1}\right)\) on parabola and focus \(F(a, 0)\) be \(Q(h, k)\). Then, \(\quad(h, k)=\left(\frac{x_{1}+a}{2}, \frac{y_{1}+0}{2}\right)\)…