x^2+y^2=36 graph equation describe the graph and its lines of symmetry

Aziz is correct except I would like to point out that all lines that pass through the centre of the circle (0,0) will be an axis of symmetry.

Circles have an infinite number of axes of symmetry.  

x^2 + y^2 = 36 is the in the form of x^2 + y^2 = r^2 which is a circle with radius, r. In this case, we have a radius of 6 [36 = r^2 --> r = sqrt(36) = 6] and center at the origin (0,0) [since there is only x^2 and y^2 and not 5x^2 and 4y^2)]. 

To graph this, you can solve for y in terms of x:

x^2 + y^2 = 36 --> 

36 - x^2 = y^2 -->

sqrt(36 - x^2) = sqrt(y^2) -->

y = +/- sqrt(36-x^2)

Notice, we have two half-circles since we took both the positive and negative square root of 36-x^2.

This graph is a circle with a center at the origin (0,0) and a radius of 6. The lines of symmetry include the x-axis and the y-axis.