How to find the Radius and Center of a Circle from its equation
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
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Solved EXAMPLE 2 on how to find an Equation of a Circle if its Center and Radius-length is given