Eliminate the parameter in the parametric equations x =4 + sine t, y=6 + sine t, for 0≤t ≤pi/2 , and describe the curve, indicating its positive orientation. how does this curve differ from the curve x=4 + sine t, y= 6 + sine t, for pi/2 ≤t ≤pi ?

It is given that

Subtracting both the above equations we get

It is equation of a straight line.

The curve is drawn in the attached figure.

c)

The first curve is defined for 'x' ranging from 4 to 5 and 'y' ranging from 6 to 7 while as

The second curve is defined for 'x' ranging from 5 to 4 and 'y' ranging from 7 to 6

Since range and domain of both the curves is same thus they represent the same region.

option a is correct.

step-by-step explanation:

scale factor: it is used to find proportional measurements.

proportions means having the same ratio.

scale factor is the ratio of the model measurement to the actual measurement in a simplest form.

or we can say that the ratio of any two corresponding lengths in two similar geometric figures

if the scale factor is more than 1, then it is an enlargement,

if the scale factor less than 1, then it is a reduction.

given the two geometric figure:

by definition of proportions, we have