Eliminate the parameter and write the corresponding rectangular equation whose graph represents the curve.

Question

(a)  sketch  the  curve  represented  by  the parametric equations (indicate the orientation of the curve) and (b) eliminate the parameter and write the corresponding rectangular  equation  whose  graph  represents  the  curve. Adjust  the  domain  of  the  resulting  rectangular equation  if necessary.

x = 1/4 t

y = t^2

Answer 1

Step 1:

(a)

The parametric equations are and .

Draw a table for different values of .

Graph:

Draw the coordinate plane.

Plot the point obtained from the table.

Connect the points to a smooth curve.

Solution:

(a) Graph of the parametric curve is

Answer 2

Step 1:

(b)

The parametric equations are and .

Consider .

Substitute in .

Rectangular equation of the curve is .

Solution:

(b) Rectangular equation of the curve is .