A point $(\alpha, \beta)$ lies on a circle $x^2+y^2=1$, then locus of the point $(3\alpha +2\beta)$ is a$/$an.

Point will be $(3\alpha ,2\beta )$ not $( 3\alpha +2\beta )$

Now $x^{2}+y^{2}=1$

Radium is $1$ unit,hence parametric co - ordinate is

$(\alpha ,\beta )= (1\cos\theta ,1\sin\theta )=(\cos\theta , \sin\theta )$

Hence

Point is $(3\cos\theta ,2\sin\theta )$

Hence

$(x,y)= (3\cos\theta ,2\sin\theta )$

$x=3\cos\theta$

$\Rightarrow \dfrac{x}{3}\cos\theta$ ...(i)

$y=2\sin\theta$

$\Rightarrow \dfrac{y}{2} = \sin \theta$ ...(ii)

$(i)^{2} + (ii)^{2}$

$\dfrac{x^{2}}{9} + \dfrac{y^{2}}{4} \cos^{2}\theta + \sin^{2} \theta$

$\dfrac{x^{2}}{9}+ \dfrac{y^{2}}{4} = 1$

which is equation of ellipse