Question

how do you sketch the curve represented by
x=(√t2+2)
y=t/4?

Answer 1

just like the other one!
pick some values for t, calculate x and y, and plot the points.

First, decide whether you meant

x=?(t^2+2)
or
x=?t^2 + 2)

I suspect the former, since ?t^2 = |t|

So, x is basically just t
y is basically just t.

The graph will be almost a straight line as x gets large. To wit:

http://www.wolframalpha.com/input/?i=parametric+plot+x%3D%E2%88%9A(t%5E2%2B2),+y%3Dt%2F4

Looks like a branch of an hyperbola, no? Let's see

t = 4y
x=?(t^2+2)
=?(y^2/16+2)
x^2 = y^2/16 + 2
x^2/2 - y^2/32 = 1

Yep - an hyperbola. For large x, the graph approaches the asymptotes.

Answer 2

you can either
(a) find and fix my typo
(b) read bobpursley's solution, which is correct.