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Question: Answered & Verified by Expert
The orthocenter of the triangle formed by the lines $x-2 y=10$ and $6 x^2+x y-y^2=0$ is
MathematicsStraight LinesMHT CETMHT CET 2022 (06 Aug Shift 1)
Options:
  • A $(2,-4)$
  • B $(2,4)$
  • C $(-2,-4)$
  • D $(-2,4)$
Solution:
2211 Upvotes Verified Answer
The correct answer is: $(2,-4)$
$\begin{aligned} & 6 x^2+x y-y^2=0 \\ & \Rightarrow(2 x+y)(3 x-y)=0 \\ & \Rightarrow 3 x-y=0 \text { and } 2 x+y=0 \text { and } x-2 y=10 \\ & \because 2 x+y=0 \text { and } x-2 y=10 \text { are perpendicular }\end{aligned}$
Hence, orthocentre is point of intersection $2 x+y=0$ and $x-2 y=10$ i.e. $(2,-4)$

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