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COMEDK · Maths · 10. Straight Lines

The locus of the mid-point of the intercept of the line \(x \cos \alpha+y \sin \alpha=p\) between the coordinate axes is

  1. A \(x^{-2}+y^{-2}=4 p^{-2}\)
  2. B \(x^{-2}+y^{-2}=p^{-2}\)
  3. C \(x^{2}+y^{2}=4 p^{-2}\)
  4. D \(x^{2}+y^{2}=p^{2}\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(x^{-2}+y^{-2}=4 p^{-2}\)

Step-by-step Solution

Detailed explanation

Given, line segment is \(x \cos \alpha+y \sin \alpha=p\) Therefore, it cuts the \(X\)-axis and \(Y\)-axis at points \((p \sec \alpha, 0)\) and \((0, p \operatorname{cosec} \alpha)\). Hence, the coordinate of the mid point are…