SOLUTION: Find an expression for the top half of the circle x^2 + (y - 2)^2 = 4.

Algebra ->  Equations -> SOLUTION: Find an expression for the top half of the circle x^2 + (y - 2)^2 = 4.      Log On


   

Question 1083696: Find an expression for the top half of the circle x^2 + (y - 2)^2 = 4.
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

x%5E2+%2B+%28y+-+2%29%5E2+=+4
This is the equation of a circle. So we are looking to find an expression for the function that is the top half of the circle.
Functions are usually written in the form:
y = something; so, solve given equation for y
x%5E2+%2B+%28y+-+2%29%5E2+=+4.....add -x%5E2 to both sides
x%5E2+-x%5E2%2B+%28y+-+2%29%5E2+=+-x%5E2%2B4
%28y+-+2%29%5E2+=+-x%5E2%2B4.....take sqrt of both sides
sqrt%28%28y+-+2%29%5E2%29+=+sqrt%28-x%5E2%2B4%29
y+-+2+=+sqrt%28-x%5E2%2B4%29
y+=+sqrt%28-x%5E2%2B4%29%2B2
so, the top half of the circle is +sqrt%28-x%5E2%2B4%29%2B2
and the bottom half of the circle is +-sqrt%28-x%5E2%2B4%29%2B2

here is a graph of the top half of the circle

+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+sqrt%28-x%5E2%2B4%29%2B2%29+

here is a graph of the bottom half of the circle

+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+-sqrt%28-x%5E2%2B4%29%2B2%29+

here is a graph of the whole circle