How do you find the equation for the of the top half of a circle with radius 3?

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Answer 1 · 2018-03-16T22:43:56

Solve for #y# and choose the positive square root to get an equation like:

#y = sqrt(9-x^2)#

The equation:

#x^2+y^2 = 3^2#

describes a circle of radius #3# centred at the origin.

If we attempt to solve for #y#, then we can proceed as follows:

Subtract #x^2# from both sides to get:

#y^2 = 9-x^2#

Take the square root of both sides to find:

#y = +-sqrt(9-x^2)#

Note that this gives us two values for #x in (-3, 3)# as we might expect - one value above the #x# axis and the other below.

Since we are only interested in the upper half, we can select the non-negative square root to get the equation:

#y = sqrt(9-x^2)#

graph{sqrt(9-x^2) [-10, 10, -5, 5]}