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AP EAMCET · Maths · Straight Lines

If a pair of perpendicular lines through the origin together with the straight line \(2 x+3 y=6\) form an isosceles triangle, then the area of that triangle (in sq units) is

  1. A \(\frac{6}{\sqrt{13}}\)
  2. B \(\frac{6}{13}\)
  3. C \(\frac{36}{13}\)
  4. D \(\frac{27}{13}\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(\frac{36}{13}\)

Step-by-step Solution

Detailed explanation

Since, \(\triangle A O B\) is a right angled triangle, so \[ \angle A=\angle B=\frac{\pi}{4} \] \[ \begin{aligned} So, \quad & A B=2 A P=2 O P \\ Now, \quad & O P=\frac{|6|}{\sqrt{4+9}}=\frac{6}{\sqrt{13}} \end{aligned} \] So, Area of…