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TS EAMCET · Maths · Straight Lines

The combined equation of the three sides of a triangle is \(\left(x^2-y^2\right)(2 x+3 y-6)=0\). If the point \((0, \alpha)\) lies in the interior of this triangle, then

  1. A \(-2 < \alpha < 0\)
  2. B \(-2 < \alpha < 2\)
  3. C \(0 < \alpha < 2\)
  4. D \(\alpha \geq 2\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(0 < \alpha < 2\)

Step-by-step Solution

Detailed explanation

The sides of a triangle are given by \( \left(x^2-y^2\right)(2 x+3 y-6)=0 \) or \( x-y=0, x+y=0,2 x+3 y-6=0 \) We observe that the point \((0, \alpha)\) moves on \(x=0\). Thus, the value of \(\alpha\) lies between \(0 < \alpha < 2\).