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Circle equation calculator

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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.

About calculator

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.

Finding 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.

Example 1

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

circle with center (2,1) and radius 3

Example 2

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.

circle with center (1,-3) and radius 1

Finding circle equation

Example 3

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

Circle equation calculator
circle equation ⇒ center and radius
help ↓↓ examples ↓↓
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Circle equation calculator
center and radius ⇒ circle equation
help ↓↓ examples ↓↓
Find the equation of a circle in form, with a center at and
Hide graph
Find approximate solution
Examples
ex 1:
Find the center and the radius of the circle (x-3)2+(y+2)2 = 16.
ex 2:
Find the center and the radius of the circle x2+y2+2x-3y-3/4=0.
ex 3:
Find the equation of a circle in standard form, with a center at C(-3,4) and passing through the point P(1,2).
ex 4:
Find the equation of a circle in standard form, with a center at C(1/2, -3/2) and a radius of r = 5.
Find more worked-out examples in our database of solved problems.
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