Question

For $X\in [-2\pi ,3\pi ]andy\in R$ the number of ordered pair satisfying equation $(\sqrt{3}\sin x-\cos x-3y^2+6y-5)=0$ will be

• A. 8
• B. 4
• C. 6
• D. 3

Answer 1

The correct option is D 3

Given equation can be converted to
$2\sin (x-\pi /6)=3(y-1{)}^2+2$
$\because L.H.S\le 2andR.H.S\ge 2$
$\Rightarrow L.H.S=R.H.S=2$
$\Rightarrow x=(4n+1)\frac{\pi }{2}+\frac{\pi }{6},n\in Iandy=1$
$X\in [-2\pi ,3\pi ]\Rightarrow x=-\frac{4\pi }{3},\frac{2\pi }{3},\frac{8\pi }{3}$
$soNo.oforderedpair=3$