Question

Consider the following x=t 1 y = --- 6 (a) Sketch the curve represented by the parametric equations (indicate the orientation of the curve). у у 10 10 5 - 10 -5 5 X 10 - 10 - 5 5 5 10 10 o у 10 10 Unread Ant Innated 10 5 10 5 X 10 10 5 10 10 (b) Eliminate the parameter and write the resulting rectangular equation whose graph represents the curve. Adjust the domain of the rectangular equation, if necessary 0 (0,00) O [0, 0) O (-1/6, O (-1/6, ) O not necessary

Answer 1

To sketch the curve, plot the points obtained by plugging in different values of t and connect them. To eliminate the parameter, equate x = t to x and solve for t. The resulting rectangular equation is y = -6x.

Step-by-step explanation:

(a) Sketching the Curve:

To sketch the curve represented by the parametric equations, we can plot the points obtained by plugging in different values of t. For example, when t = 0, x = 0 and y = 0. When t = 1, x = 1 and y = -1/6.

By plotting these points and connecting them, we can sketch the curve. The orientation of the curve can be determined by analyzing the values of x and y for different values of t.

(b) Eliminating the Parameter:

To eliminate the parameter t and write the resulting rectangular equation, we can equate x = t to x and solve for t. This gives us t = x. Substituting this value back into the equation for y gives us y = -6x.

Therefore, the resulting rectangular equation is y = -6x. The domain of this equation is all real numbers.