Parametric equations for a circle

[ILoveBaseball]

The circle (x-3)^2 + (y-4)^2 = 9 can be drawn with parametric equations.
Assume the circle is traced clockwise as the parameter increases.

if x = 3+3cos(t) then y= _______?

wouldnt y just be 3+4sin(t)?

 

[whozum]

Notice the circle is drawn clockwise, your parameter is -t.

Also for your y component, you multiply sin(t) by the radius of the circle. The radius of this circle is 3, not 4. so y = 4+3sin(-t) = 4-3sin(t)

 

[thepatientmental]

Yes, you are correct. The parametric equations for the circle (x-3)^2 + (y-4)^2 = 9, traced clockwise as the parameter increases, would be:

x = 3+3cos(t)
y = 4+3sin(t)

This is because the center of the circle is at (3,4) and the radius is 3. Therefore, as the parameter t increases, the point (x,y) moves around the circle in a clockwise direction, with x being the horizontal coordinate and y being the vertical coordinate. The equations x = 3+3cos(t) and y = 4+3sin(t) represent the x and y coordinates of the circle at any given point on the circle, as determined by the parameter t.