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!

Step-by-step 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:

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

⇒ $(0-2)^2+(y-3)^2=16$

⇒ $4+(y-3)^2=16$

⇒ $(y-3)^2=12$

⇒ $\sqrt{(y-3)^2}=\sqrt{12}$

⇒ $y-3 = \pm 2\sqrt{3}$

⇒ $y=3 \pm 2\sqrt{3}$

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