Answer
$34X^2+41Y^2+24XY=400$
Work Step by Step
Here, we have $x=X \cos \phi -Y\sin \phi$ and $y=X \sin \phi+Y \cos \phi$
$\sin \phi =\dfrac{3}{5}$ and $\cos \phi =\dfrac{4}{5}$
$x=X (\dfrac{3}{5}) -Y (\dfrac{4}{5}) \implies x=\dfrac{4X-3Y}{5}$
and $y=X (\dfrac{4}{5})+Y (\dfrac{3}{5}) \implies y=\dfrac{3X+4Y}{5}$
$x^2+2y^2=16$
This gives: $(\dfrac{4X-3Y}{5})^2+2\dfrac{3X+4Y}{5}^2=16$
Thus, $34X^2+41Y^2+24XY=400$
