This calculator can find the center and radius of a circle given its equation in standard or general form. Also, it can find equation of a circle given its center and radius. The calculator will generate a step by step explanations and circle graph.
This calculator solves two types of problems. The first one is how to find the center and radius if we know an equation. The second problem is how to find the circle equation if we know the circle center and radius.
The standard circle equation has the form
(x-h)2+(y-k)2=r2
where r is a radius and (h,k) is the center of a circle.Find the center, and the radius of a circle
(x-2)2+(y-1)2=9
To find the center we just need to change the sign of the numbers in the brackets, so
C(2,1)
To find the radius we need to take a square root of 9.
r = √9 = 3
Find the center, and the radius of a circle
x2+y2-2x+6y+9=0
In this example we need to transform the circle equation into standard form:
x2+y2-2x+6y+9=0
x2-2x+1 + y2+6y+9 = -9 + 9 + 1
(x-1)2+(y+3)2=1
Like in the previous example, we can conclude that the center is point C(1,-3) and the radius is r=1.
Find the circle equation if the center is point C(-3,5) and the radius is r=4.
To solve this problem, we will use standard circle equation with h=-3, k=5 and r = 4.
(x-h)2+(y-k)2=r2
(x-(-3))2 + (y-4)2 = 422
(x+3)2+(y-4)2 = 16
The general equation of a circle is:
(x+3)2+(y-4)2 = 16
x2+6x+9 + y2-8y+16 = 16
x2 + y2 +6x - 8y + 9 = 0
1. Identifying the Center & Radius — lesson with worked examples.
2. Youtube tutorial center and radius of a circle in standard form.