Find Radius and Center from Circle Equation (e.g 2)

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

Click here for EXAMPLE 1

EXAMPLE 2: What is the center and radius of  

-9 = – y² – x²?

SOLUTION:

The standard equation of a circle is:

(x – h)² + (y – k)² = r² ————————(1)

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

Here, we have

-9 = – y² – x²   (given)

Flip the equation 

– x² – y² = – 9 

Take -1 common on both sides of equal sign

 -1( x² + y²) = -1(9)

Cancel -1 on both sides of equal sign

x² + y² = 9

This equation can be written as

(x – 0)² + (y – 0)² = 3² ————————(2)

Compare equation (1) and equation (2)

we get

h = 0

k = 0

r = 3

Thus, the circle whose equation is -9 = – y² – x²

 has center (h, k) at (0, 0)

And its radius r is 3