Question
how do you sketch the curve represented by
x=(√t2+2)
y=t/4?
x=(√t2+2)
y=t/4?
Answers
Steve
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.
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.
Steve
you can either
(a) find and fix my typo
(b) read bobpursley's solution, which is correct.
(a) find and fix my typo
(b) read bobpursley's solution, which is correct.