AP EAMCET · Maths · Straight Lines
If the straight lines \(2 x+3 y-1=0\), \(x+2 y-1=0\) and \(a x+b y-1=0\) form a triangle with orthocentre at the origin, then \((a, b)=\)
- A \((-8,8)\)
- B \((0,7)\)
- C \((6,4)\)
- D \((-3,3)\)
Answer & Solution
Correct Answer
(A) \((-8,8)\)
Step-by-step Solution
Detailed explanation
Equation of line perpendicular to line \(a x+b y-1=0\) and passes through the origin is \[ b x-a y=0 \] Now, altitude (i) passes through the intersection of lines \(2 x+3 y-1=0\), and \(x+2 y-1=0\) So, \[ \begin{aligned} -b-a & =0 \\ a+b & =0 \end{aligned} \] Due to relation…
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