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If a point $P$ on the line $3 x+5 y=15$ is equidistant from the coordinate axes, then $P$ lies
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The correct answer is:
either in first or in second quadrant
Let the point $P(h, k)$ lie on the line $3 x+5 y=15$
Distance from coordinate axes are equal from $P$.
$\therefore \quad|h|=|k|$
$\Rightarrow \quad h= \pm k$
Point $P$ line of $3 x+5 y=15$
$3 h+5 k=15 \Rightarrow 3 h+5 h=15$
$\Rightarrow \quad h=15 / 8 \Rightarrow k=15 / 8$
Put $k=-h$,
$3 h-5 h=15=h=\frac{-15}{2}, k=\frac{15}{2}$
$\left(\frac{15}{8}, \frac{15}{8}\right)$ lie in first quadrant and $\left(\frac{-15}{2}, \frac{15}{2}\right)$ ie in second quadrant.
$\therefore P$ lies in the first or in second quadrant.
Distance from coordinate axes are equal from $P$.
$\therefore \quad|h|=|k|$
$\Rightarrow \quad h= \pm k$
Point $P$ line of $3 x+5 y=15$
$3 h+5 k=15 \Rightarrow 3 h+5 h=15$
$\Rightarrow \quad h=15 / 8 \Rightarrow k=15 / 8$
Put $k=-h$,
$3 h-5 h=15=h=\frac{-15}{2}, k=\frac{15}{2}$
$\left(\frac{15}{8}, \frac{15}{8}\right)$ lie in first quadrant and $\left(\frac{-15}{2}, \frac{15}{2}\right)$ ie in second quadrant.
$\therefore P$ lies in the first or in second quadrant.
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