Question

Which is the correct calculation of the y-coordinate of point A? 0 (0 - 0)2 + (1 - y2 = 2 O (0 - 1)² + (0- y2 = 22 (0-0)² + (1 - y2 = 2 (0 - 1)2 + (0-y2 = 2​

Answer 1

The y-coordinate of point A is
`√(3)`.

Explanation:

The equation of the circle is represented by the following expression:

`(x-h)^(2)+(y-k)^(2) = r^(2)` (1)

Where:

`x` - Independent variable.

`y` - Dependent variable.

`h`,
`k` - Coordinates of the center of the circle.

`r` - Radius of the circle.

If we know that
`h = 0`,
`k = 0` and
`r = 2`, then the equation of the circle is:

`x^(2) + y^(2) = 4` (1b)

Then, we clear
`y` within (1b):

`y^(2) = 4 - x^(2)`

`y = \pm \sqrt{4-x^(2)}` (2)

If we know that
`x = 1`, then the y-coordinate of point A is:

`y = \sqrt{4-1^(2)}`

`y = √(3)`

The y-coordinate of point A is
`√(3)`.