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AP EAMCET · Maths · Straight Lines

A line \(L\) through \(A(-5,-4)\) meets the lines \(x+3 y+2=0\) and \(2 x+y+4=0\), \(x-y-5=0\) at points \(B, C\) and \(D\) respectively. If \(\left(\frac{15}{A B}\right)^2+\left(\frac{10}{A C}\right)^2=\left(\frac{6}{A D}\right)^2\), then find the equation of \(L\)

  1. A \(2 x+3 y+22=0\)
  2. B \(5 x-4 y+7=0\)
  3. C \(3 x-2 y+3=0\)
  4. D \(3 x-2 y+7=0\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(2 x+3 y+22=0\)

Step-by-step Solution

Detailed explanation

Let equation of line passing through \(A(-5,-4)\) is given by \[ \frac{x-(-5)}{\cos \theta}=\frac{y-(-4)}{\sin \theta}=r \Rightarrow \frac{x+5}{\cos \theta}=\frac{y+4}{\sin \theta}=r \] Therefore, every point on the line is of the form…