Question

A point on the straight line, $3x+5y=15$ which is equidistant from the coordinate axes will lie only in:

• A. $1^{st}$ and $2^{nd}$ quadrants
• B. $4^{th}$ quadrant
• C. $1^{st},2^{nd}$ and $4^{th}$ quadrant
• D. $1^{st}$ quadrant

Answer 1

Answer: (A)

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