How to obtain parametric equation(s) of x^2+y^2-4x=0?

Question

ganeshie8 · Answer

HINT : complete the square

mpj4 · Answer

(x-2)^2+y^2=4?

mpj4 · Answer

I do not know what kind of answer I should be getting though

welshfella · Answer

parametris equations are like x = t^2 , y = 2t  are third variable is introduced

mpj4 · Answer

So I have to show that this is a circle using that third variable?

ganeshie8 · Answer

$x-2 ~=~ 2\cos t$
$y ~= ~2\sin t$

ganeshie8 · Answer

$x~ =~2+2\cos t$
$y~=~2\sin t$

mpj4 · Answer

Would it be ok to ask on how that happened?

welshfella · Answer

the parametric equations for a circle with the centre at the origin  sre
y = sin t, x = cos t

ganeshie8 · Answer

mpj4 · Answer

Thanks

ganeshie8 · Answer

You have
$$(x-2)^2+y^2=4$$

Notice that plugging in $x=2+2\cos t$ makes the first term equal to $4\cos^2 t$

ganeshie8 · Answer

plugging in $y = 2\sin t$ gives
$$4\cos^2t + 4\sin^2t = 4$$

ganeshie8 · Answer

then use the identity $\cos^2t+\sin^2 t = 1$

mpj4 · Answer

ugh... thanks anyway. You lost me on the last part there. It's ok, you don't need to bother explaining. I'll be closing this.