AP EAMCET · Maths · Pair of Lines
The orthocentre of the triangle formed by the lines \(x+y=1\) and \(2 y^2-x y-6 x^2=0\) is
- A \(\left(\frac{4}{3}, \frac{4}{3}\right)\)
- B \(\left(\frac{2}{3}, \frac{2}{3}\right)\)
- C \(\left(\frac{2}{3}, \frac{-2}{3}\right)\)
- D \(\left(\frac{4}{3}, \frac{-4}{3}\right)\)
Answer & Solution
Correct Answer
(A) \(\left(\frac{4}{3}, \frac{4}{3}\right)\)
Step-by-step Solution
Detailed explanation
Given that, \(x+y=1\) and \(2 y^2-x y-6 x^2=0\) \(\begin{aligned} & \Rightarrow \quad 2 y^2-4 x y+3 x y-6 x^2=0 \\ & \Rightarrow \quad(2 y-3 x)+(y-2 x)=0 \\ & \Rightarrow \quad 2 y+3 x \text { and } y-2 x=0 \end{aligned}\) \(\therefore \quad\) Equation of sides are…
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