question_answer

A point on the line \[3x+5y=15\] and equidistant from the coordinate axes, lies in

A) None of the quadrants

B) Quadrants I and II only

C) Quadrant I only

D) Quadrants I, II, and III only

Correct Answer: C

Solution :

The equation of the given straight line is \[3x+5y=15\] \[\Rightarrow \]               \[\frac{x}{5}+\frac{y}{3}=1\] If the point \[P(x=y),\] lie on the straight line and equidistant from the coordinate axes, then its co-ordinates will be \[\left( \frac{15}{8},\frac{15}{8} \right)\]. Hence the required point \[P\left( \frac{15}{8},\frac{15}{8} \right)\] lies in the I Quadrant only.