Question $1$: A velocity field is given by vec$(V)=\frac{x}{a+t}i+\frac{y}{b+ct}j,$ where $a=b=1s$ and $c=2.$

$($a$)$ Find the equation of the streamline of a particle that passes through the point $(x,y)=(1,1).$

$($b$)$ Show that the equation for the pathline of a particle that passes through $(1,1)$ at $t=0$ is

$y^2=2x-1$