What is the shape of the graph of the following parametric equations x=2cost+4 and y=2 sin t-5

A circle of radius 2 around the point (4, - 5)

Step-by-step explanation:

I guess the equations are:

X = 2*cos(t) + 4

Y = 2*sin(t) - 5

Let's try some values and see where we get from that:

If t = 0°

X = 2 + 4 = 6

Y =  0 - 5 = -5

if t = 90°

X = 0 + 4

Y = 2 - 5 = -3

If t = 180°

X = - 2 + 4 = -2

Y = 0 - 5 = - 5

if t = 270°

X = 0 + 4 = 4

Y = -2 - 5 = -7

Now, if you graph those points you will see that we are creating a circle of radius 2 around the point (4, -5)

Actually, always when we have a equation:

X = R*cin(x) + a

Y = R*sin(x) + b

the graph will be a circle of radius R around the point (a,b)