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

`y = \pm √(31.59) = \pm 5.62`

So we have two points for the solution:

`(2.1, √(31.59)) , (2.1, -√(31.59))`

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 = √(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 √(31.59) = \pm 5.62`

So we have two points for the solution:

`(2.1, √(31.59)) , (2.1, -√(31.59))`