question_answer

A point on the straight line,\[3x+5y=15\]which is equidistant from the coordinate axes will lie only in: [JEE Main 8-4-2019 Morning]

A) 1st and 2nd quadrants

B) 4th quadrant

C) 1st, 2nd and 4th quadrant

D) 1st quadrant

Correct Answer: A

Solution :

Now,\[\left| \frac{15-3t}{5} \right|=|t|\] \[\Rightarrow \]\[\frac{15-3t}{5}=t\]or\[\frac{15-3t}{5}=-t\] \[\therefore \]\[t=\frac{15}{8}\]or\[t=\frac{-15}{2}\] So, \[P\left( \frac{15}{8},\frac{15}{8} \right)\in {{\text{I}}^{\text{st}}}\]quadrant or \[P\left( \frac{-15}{2},\frac{15}{2} \right)\in \text{I}{{\text{I}}^{\text{nd}}}\]quadrant