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Find Center and Radius from Equation of Circle (e.g 1)

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How to find the Center and Radius of a Circle from its Standard Equation

Click here for EXAMPLE 2

EXAMPLE 1: Find the center and radius of a circle 

(x – 1)² + (y – 4)² = 16

SOLUTION:

Detailed solved example on how to find the Center and Radius of a Circle if Equation of the circle is given


The standard equation of a circle is:

(x – h)² + (y – k)² = r²  

where (h, k) is the center of a circle and r is the radius of a circle.


Compare the given equation with the standard equation of a circle.

Detailed solved example on how to find the Center and Radius of a Circle if Equation of the circle is given
we get

h = 1
k = 4

So, center of a given circle = (h, k) = (1, 4)

and
r² = 16 
⇒ either r = +4 or r = – 4        (By taking square root on both sides)

Since r is the length and length cannot be negative, so radius r of a given circle is 4.

Thus, the circle whose equation is (x – 1)² + (y – 4)² = 16 has center at (1, 4) and its radius is 4.

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