What Is the Equation of a Circle?
The equation of a circle with its center at (x0,y0) and with radius r is given by
This means that all values for (x,y) that fulfill the equation are on the circle boundary.
To find the radius of the circle you can use this formula:
You are working with a circle with its center at (−1, 2). The point (3, 5) is on the circle boundary. What is the radius of this circle?
Here you have (x0,y0) = (−1, 2) and the point on the circle is (x,y) = (3, 5). The radius of the circle is therefore
Show that x2 + 6x + y2 − 2y − 6 = 0 is a circle
To show this, you have to use the method to complete the square. You add and subtract (b 2 ) 2 for both the x-terms and the y-terms. You then get the following:
You can see from this that x2 + 6x + y2 − 2y − 6 = 0 is a circle with its center at (−3, 1) and a radius r = 4.