how do you sketch the curve represented by
x=(√t2+2)
y=t/4?
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.
you can either
(a) find and fix my typo
(b) read bobpursley's solution, which is correct.
To sketch the curve represented by the equations x = √(t^2 + 2) and y = t/4, you will follow these steps:
1. Choose a range of values for t: Since t represents the parameter for the curve, you need to select a range of values for t that will give you a good representation of the curve. Let's say you choose -10 to 10.
2. Substitute the chosen values of t into the equations to compute the corresponding x and y values for each t value. For example, if t = -10, substitute this value into the equations:
x = √((-10)^2 + 2) = √(100 + 2) = √102
y = -10/4 = -2.5
3. Repeat this process for each chosen value of t. Compute the corresponding x and y values.
4. Plot the obtained x and y values on a coordinate plane. Use the t values as the independent variable.
5. Connect the plotted points to form a smooth curve. You may use a ruler or freehand drawing, depending on your preference and accuracy requirements.
6. Remember to label the axes and any important points on the curve, such as intersections, asymptotes, or critical points.
By following these steps, you should be able to sketch the curve represented by the given equations.