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equation of a circle

I've converted: x = 1+2cost , y = 3+2sint

into: cos^2(t) = ((x-1)/2)^2 , sin^2(t) = ((y-3)/2)^2

using sin^2 + cos^2=1 identity: ((x-1)/2)^2 + ((y-3)/2)^2 = 1

I have to sketch the circle but I don't know what to do with the denominators being 2, can I multiply everything by 2 or is the 2 protected by the power?

Reply 1

UPSDGoat

((x-1)/2)^2 + ((y-3)/2)^2 = 1

Is the same as

(1/2)^2(x-1)^2+(1/2)^2(y-3)^2=1

So squaring and factorising gets you (1/4)((x-1)^2+(y-3)^2)=1

So the equation of the circle would be:-
(x-1)^2+(y-3)^2=4
once you multiply both sides by 4