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?

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?

1 Answer

Impact of this question

2392 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-06-05T03:59:59

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

Explanation:

${(x - 1)}^{2} + y^{2} = 1$ $(x-1)^2+y^2 =1$

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

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

By definition,

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

Now, $P$ $P$ can move around the circle as $θ \in [0, 2 π]$ $theta in [0, 2pi]$

Hence, $x + y = 1 + cos θ + sin θ$ $x+y = 1+cos theta +sin theta$ for $θ \in [0, 2 π]$ $theta in [0,2pi]$

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

Let $θ = 0 \to x + y = 1 + 1 + 0 = 2$ $theta =0 -> x+y = 1+1+0=2$
which is of course the diameter of the circle.

Science

Math

Humanities

... and beyond

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?

1 Answer

Explanation:

Related questions

Impact of this question