JEE Mains · Maths · STD 11 - 9. straight line
Consider the set of all lines \(px + qy + r = 0\) such that \(3p + 2q + 4r = 0\) . Which one of the following statements is true?
- A The lines are concurrent at the point \(\left( {\frac{3}{4},\frac{1}{2}} \right)\)
- B Each line passes through the origin.
- C The lines are all parallel
- D The lines are not concurrent
Answer & Solution
Correct Answer
(A) The lines are concurrent at the point \(\left( {\frac{3}{4},\frac{1}{2}} \right)\)
Step-by-step Solution
Detailed explanation
\(px + qy + r = 0\) \(px + qy + \left( {\frac{{ - 3p - 2q}}{4}} \right) = 0\) \(p\left( {x - \frac{3}{4}} \right) + q\left( {y - \frac{2}{4}} \right) = 0\) \(x = \frac{3}{4}\,\,\) and \(y = \frac{1}{2}\)
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