Question

Let $2x-3y=0$ be a given line and $P(\sin \theta ,0)$ and $Q(0,\cos \theta )$ be the two points. Then $P$ and $Q$ lie on the same side of the given line, if $\theta$ lies in the

• A. 1st quadrant
• B. 2nd quadrant
• C. 3rd quadrant
• D. none of these

Answer 1

The correct option is A 1st quadrant

Given line

$2x-3y=0$

Point P and Q lie on same side Hence by position of point w.r. to line

On passing P$(\sin \theta ,0)$

$2\sin \theta >0$

$\theta >0---\left(1\right)$

On passing Q$(0,\cos \theta )$

$-3\cos \theta >0$

$\cos \theta <0$

$\theta <\frac{\pi }{2}-----\left(2\right)$

On combining both (1) and (2)

$0<\theta <\frac{\pi }{2}$

Hence $\theta$ lies in $1st$ quadrant