Question

The radius of the circle whose equation in parametric form is

P(x)= (acosx+bsinx , asinx -bcosx)

Answer 1

so the graph is
P(x) = ( acos x + bsin x , a sin x - b cos x )

Answer 2

it probably makes more sense to use 't' as the parameter, but in any case

Answer 3

let me graph it in parametric mode on my calculator

Answer 4

actually it was theta , but i couldn't type the symbol so i used x

Answer 5

im going to use 't' as the parameter ,

P(t)= (acost+bsint , asint -bcost)

Answer 6

okay

Answer 7

lets represent theta by t then :)

Answer 8

so we have
P(t) = (x(t), y(t))
where
x(t) = a cos t + b sin t
y(t) = a sin t - b cos t

first impulse is to square x and y

x^2 + y^2 = ( a cos t + b sin t ) ( a sin t - b cost )
= a^2 cos t sin t + a*b sin^t - a*b cos^2 t - b^2 cos t sin t

Answer 9

that should stay a*b sin^2(t)

Answer 10

yes then

Answer 11

i got an idea....

Answer 12

actually lets solve for x^2 separately

Answer 13

x^2 = a^2 cos^2 (t) + b^2 * sin^2(t) + acos(t)*b*sint(t)

Answer 14

The next thing to do is pretty obvious