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TS EAMCET · Maths · Pair of Lines

The centroid of the triangle formed by the lines \(x+y=1\) and \(2 y^2-x y-6 x^2=0\) is

  1. A \((0,0)\)
  2. B \(\left(\frac{5}{9}, \frac{11}{9}\right)\)
  3. C \(\left(\frac{-5}{9}, \frac{11}{9}\right)\)
  4. D \(\left(\frac{5}{9}, \frac{-11}{9}\right)\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(\left(\frac{-5}{9}, \frac{11}{9}\right)\)

Step-by-step Solution

Detailed explanation

We have, \(\begin{array}{rlrl} & & 2 y^2-x y-6 x^2 & =0 \\ \Rightarrow & & 2 y^2-4 x y+3 x y-6 x^2 & =0 \\ \Rightarrow & 2 y(y-2 x)+3 x(y-2 x) & =0 \\ \Rightarrow & & (y-2 x)(2 y+3 x) & =0 \end{array}\) \(\therefore\) Equations of sides of triangle are \(x+y=1\),…