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AP EAMCET · Maths · Straight Lines

The square of the distance from the origin to the point of intersection of the pair of lines \(a x^2+2 h x y-a y^2+2 g x+\) \(2 \mathrm{fy}+\mathrm{c}=0\) is

  1. A \(\frac{\mathrm{f}^2+\mathrm{g}^2}{\mathrm{a}^2+\mathrm{h}^2}\)
  2. B \(\frac{\mathrm{f}^2+\mathrm{g}^2}{\mathrm{a}^2-\mathrm{h}^2}\)
  3. C \(\frac{\mathrm{f}^2+\mathrm{g}^2}{\mathrm{~h}^2-\mathrm{a}^2}\)
  4. D \(\frac{\mathrm{f}^2-\mathrm{g}^2}{\mathrm{~h}^2-\mathrm{a}^2}\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(\frac{\mathrm{f}^2+\mathrm{g}^2}{\mathrm{a}^2+\mathrm{h}^2}\)

Step-by-step Solution

Detailed explanation

The equation of pair of lines is \[ a x^2+2 h x y-a y^2+2 g x+2 f y+c=0.....(i) \] Let the lines represented by the given equation be \[ \begin{aligned} & l x+m y+n=0.....(ii) \\ & l^{\prime} x+m^{\prime} y+n^{\prime}=0.....(iii) \end{aligned} \] from eqs. (i), (ii) \& (iii)…