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
- A \(-2 < \alpha < 0\)
- B \(-2 < \alpha < 2\)
- C \(0 < \alpha < 2\)
- D \(\alpha \geq 2\)
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 \(0 < \alpha < 2\).
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