Parametric equations
transformations : let x = (2 cos t) + h and y = (2 sin t) + k
(a) writing to learn : let k=0 and h= -2,-1,1, and 2, in turn. graph
using the parameter interval [0,2(pi)]. describe the role
ofh.
(b) writing to learn : let h=0 and k= -2,-1,1, and 2, in turn. graph
using the parameter interval [0,2(pi)]. describe the role
ofk.
(c) find a parametrization for the circle with radius 5 and
centerat (2,-3)
(d) find a parametrization for the ellipse centered at (-3,4)
withsemimajor axis of length 5 parallel to the x-axis and
semiminoraxis of length 2 parallel to the y-axis.

for the points

step-by-step explanation:

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below:

y= 2x+7

changed to y= 5x +7

as slope is increased from 2 to 5

therefore it would be less steeper

so, option d) is correct