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

Answer:

The y-coordinate of point A is $\sqrt{3}$.  

Step-by-step 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:

$y = \sqrt{4-1^{2}}$

$y = \sqrt{3}$

The y-coordinate of point A is $\sqrt{3}$.