The curve represented by $x = 3\cos t + 3\sin t$ and $y = 4\cos t - 4\sin t$ is

The equations of curve are

$x =3(\cos t + \sin t)$

$\Rightarrow \dfrac {x}{3} = \cos t + \sin t .... (i)$

and $y = 4(\cos t - \sin t)$

$\Rightarrow \dfrac {y}{4}= (\cos t - \sin t) .... (ii)$

On squaring and adding (i) and (ii)

$\dfrac {x^{2}}{9} + \dfrac {y^{2}}{16} = 2 (\sin^{2}t + \cos^{2}t)$

$\Rightarrow \dfrac {x^{2}}{9} + \dfrac {y^{2}}{16} = 2$ Which is an ellipse

Hence choice (a) is correct answer.