Question

The point(s) ( 2.1 , y ) is/are on the circle x 2 + y 2 = 36 . Determine the missing coordinate(s) and enter the point(s) below. If there is more than one point, enter all points and separate the answers with a comma. Give the exact answer, using a square root symbol as appropriate. Decimals under the radical are ok.

Answer 1

Answer:

$y = \pm \sqrt{31.59} = \pm 5.62$

So we have two points for the solution:

$(2.1, \sqrt{31.59}) , (2.1, -\sqrt{31.59})$

Step-by-step explanation:

For this case have the following equation given:

$x^2 +y^2 = 36$

And if we see this equation ahve the general form of a circle given by:

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

Where the center os (0,0) and the readius $r = \sqrt{36}=6$

For this case we have a point given (2.1,y) and we are interested in find the y missing coordinate, so we jjust need to replace the point into the equation and we got:

$2.1^2 + y^2 = 36$

Now we can solve for y like this:

$y^2 = 36-2.1^2 =31.59$

And now we can take square root on both sids and we got:

$y = \pm \sqrt{31.59} = \pm 5.62$

So we have two points for the solution:

$(2.1, \sqrt{31.59}) , (2.1, -\sqrt{31.59})$