Question

If X and y satisfy the realation x-1)^2+y^2 is equal to 1 then possible value of X+y is equal to?

Answer 1

`x+y = 1+cos theta +sin theta` for `theta in [0,2pi]`
Possible value: `x+y= 2; theta=0`

Explanation:

`(x-1)^2+y^2 =1`

`f(x,y)` above is a unit circle centered at the point `(1,0)`

Now, consider a point `P` on the circle making an angle `theta` with the `x-`axis at the point `(1,0)`

By definition,

the y-component of `P` is `sin theta`
the x-component of `P` is `1+ cos theta`

Now, `P` can move around the circle as `theta in [0, 2pi]`

Hence, `x+y = 1+cos theta +sin theta` for `theta in [0,2pi]`

Since we are asked to find a "possible" value of `x+y`

Let `theta =0 -> x+y = 1+1+0=2`
which is of course the diameter of the circle.