TS EAMCET · Maths · Straight Lines
The centroid of the triangle formed by the pair of straight lines \(12 x^2-20 x y+7 y^2=0\) and the line \(2 x-3 y+4=0\) is \((\alpha, \beta)\). Then, \(\alpha+2 \beta=\)
- A \(-\frac{4}{3}\)
- B 2
- C 8
- D \(-\frac{8}{3}\)
Answer & Solution
Correct Answer
(C) 8
Step-by-step Solution
Detailed explanation
Centroid at \(12 x^2-20 x y+7 y^2=0\) (pair at straight lines) and \(2 x-3 y+4=0\) is \((\alpha, \beta)\). So, \( \begin{aligned} 12 x^2-14 x y-6 x y+7 y^2 & =0 \\ 2 x(6 x-7 y)-y(6 x-7 y) & =0 \\ 2 x-y=0,6 x-7 y & =0 \end{aligned} \) and So, centroid is…
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