What is the center and radius of #x^2+y^2=4y-11-8x#?
2 Answers
The centre of the circle is
Explanation:
Notice that although this is a circle, it isn't in the familiar form that we know:
To get it into this form, we will complete the square for both
Center:
Radius:
Explanation:
In order to not make this problem painful and difficult for ourselves, we should get it into the standard form for a circle, which is
How do we do this, you ask? Let's first get everything on one side EXCEPT the number:
Some rearranging...
....and we are ready to complete the square! If you need a refresher, we're going to create perfect square binomials. The two in our formula above are perfect square binomials. We will create them by dividing the "middle" coefficient for each variable by 2 and then squaring the result:
We're not done, though. Completing the square requires that
Hooray! We're in standard form. Let's find our answers. The center will be
Hope this helped you!