JEE Mains · Maths · STD 11 - rectangular cartensian co-ordinates
If the orthocentre of the triangle formed by the lines \(2 x+3 y-1=0, x+2 y-1=0\) and \(a x+b y-1=0\), is the centroid of another triangle, whose circumcentre and orthocentre respectively are \((3,4)\) and \((-6,-8)\), then the value of \(|a-b|\) is ........... .
- A 16
- B 15
- C 14
- D 13
Answer & Solution
Correct Answer
(A) 16
Step-by-step Solution
Detailed explanation
\(2 x+3 y-1=0\) \(x+2 y-1=0\) \(a x+b y-1=0\) \(\left(\frac{6-6}{3}, \frac{8-8}{3}\right)\) \(=(0,0)\) \(a x+b y-1=0\) \(\left(\frac{1-0}{-1-0}\right)\left(\frac{-a}{b}\right)=-1\) \(\Rightarrow- a = b\) \(\Rightarrow a x-a y-1=0\) \(a x-a\left(1-\frac{2 x}{3}\right)-1\)…
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