x^2+y^2=36 is a circle. How can you tell without actually plotting? Where is the center?
The center placed in the point (0,0)
radius = sqrt ( 36 ) = 6
ya gotta know that
(x-h)^2 + (y-k)^2 = r^2
is the equation for a circle of radius r with center at (h,k)
To determine whether x^2 + y^2 = 36 represents a circle without plotting, we can examine the equation and compare it to the general equation of a circle.
In the general equation of a circle, (x - h)^2 + (y - k)^2 = r^2, the values h and k represent the coordinates of the center of the circle, and r represents the radius.
By comparing these equations, we can deduce that the center of the circle in the equation x^2 + y^2 = 36 is (0, 0), because there are no additional terms involving x or y. When there is no specific shift of the x or y axis indicated in the equation, the center is always at the origin (0, 0).
Additionally, the radius of the circle is given by r = sqrt(36) = 6. The radius is simply the square root of the constant value on the right side of the equation.
Therefore, x^2 + y^2 = 36 represents a circle with its center at the origin (0, 0) and a radius of 6 units.