a circle with center o is shown create the equation for the circle the point is at (1,1) the top touches 1,5 the left touches -3,1
To create the equation for the circle, we first need to find the radius of the circle.
The distance between the center of the circle (O) and the point (1,1) can be found using the distance formula:
√( (1-0)^2 + (1-0)^2 ) = √2
Since the top of the circle touches the point (1,5), the distance between the center and the top point is equal to the radius of the circle:
√( (5-1)^2 + (1-1)^2 ) = √16 = 4
Therefore, the radius of the circle is 4 units.
The equation for a circle with center at point O(0,0) and radius 4 is:
(x - 0)^2 + (y - 0)^2 = 4^2
x^2 + y^2 = 16
Since the circle is translated to the point (1,1), we need to shift the origin of the equation. The new equation for the circle is:
(x - 1)^2 + (y - 1)^2 = 16