Question

Determine whether the statement is true or false.

The circle (x-2)^2+(y-3)^2=16 intersects the y-axis.
The statement is _____

Answer 1

statement is true!

Explanation:

Here we have , The circle
`(x-2)^2+(y-3)^2=16` intersect y-axis. We need to find that this statement is true or false . We have the following equation of circle :

`(x-2)^2+(y-3)^2=16`

Now, In order to say that circle intersect y-axis , we have x=0 , Let's find out value of y for this:

`(x-2)^2+(y-3)^2=16`

⇒
`(0-2)^2+(y-3)^2=16`

⇒
`4+(y-3)^2=16`

⇒
`(y-3)^2=12`

⇒
`√((y-3)^2)=√(12)`

⇒
`y-3 = \pm 2√(3)`

⇒
`y=3 \pm 2√(3)`

Therefore circle
`(x-2)^2+(y-3)^2=16` intersect y-axis at two points
`(0 , 3+2√(3))` and
`(0 , 3-2√(3))`. And so statement is true!