MA $243$

Show clear work for all solutions. Don't make any mistakes. Good luck!

In ${}^3$ sketch the surface. $[2$ each$]$

a$.y^2{z}^2=1$

b$.z-y^2-x^2=0$

Hint: Use traces. For the $xy-$trace, use $z=1$

$2.$ Find a vector equation and parametric equations for the line segment that joins the point $P(2,4,-1)$ to the point $Q(1,-2,4).[2]$

Hint: Use the fact that the line segment from $r_0$ to $r_1$ is given by the vector equation

$r(t)=(1-t)r_{0}t{r}_1$ for $0t1$

OVER $$