Question

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

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

Answer 1

Answer: (A)

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, $P\left(\frac{15}{8},\frac{15}{8}\right)\in I^{\text{st }}$ quadrant
or $P\left(\frac{-15}{2},\frac{15}{2}\right)\in {\left(II\right)}^{nd}$ quadrant