Question

The function r(t) traces a circle. Determine the radius, center, and plane containing the circle r(t)=−9i+ (11cos(t))j+ (11sin(t))k

Answer 1

we are given

r(t)=−9i+ (11cos(t))j+ (11sin(t))k

now, we can find x-components , y-component and z-component

$x=-9,y=11cos(t),z=11sin(t)$

now, we can square and add them

$x^2+y^2+z^2=(-9)^2+(11cos(t))^2+(11sin(t))^2$

now, we can simplify it

$x^2+y^2+z^2=81+121cos^2(t)+121sin^2(t)$

$x^2+y^2+z^2=81+121(cos^2(t)+sin^2(t))$

$x^2+y^2+z^2=81+121$

$x^2+y^2+z^2=202$

we can also write as

$(x-0)^2+(y-0)^2+(z-0)^2=(\sqrt{202} )^2$

now, we can compare it with

$(x-0)^2+(y-0)^2+(z-0)^2=(r )^2$

Center:

(0,0,0)

radius:

$r=\sqrt{202}$