We must get the circle in standard form:
(x - h)² + (y - k)² = r²
in order to get the radius.
4x² + 4y² - 7x + 6y - 35 = 0
4x² - 7x + 4y² + 6y = 35
Divide through by 4
x² - 
x + y² + 
y = 
x² - x + y² + 
y =
(x² - x) + (y² + y) =
Complete the square in each parentheses)
For the first parentheses:
Multiply the coefficient of x, which is 
by 
,
getting 
, then square that 
= 
Add that in the first parentheses and also add it to the right side.
For the second parentheses:
Multiply the coefficient of y, which is by ,
getting 
, then square that 
= 
Add that in the second parentheses and also add it to the right side.
(x² - x + ) + (y² + y + ) = + +
Factor each parentheses
(x - 
)² + (y - ) = + +
Get a LCD of 64 for the fractions on the right side:
+ + = 
+ + 
= 
So the center is (, ) and the radius is 
= 
. That wasn't necessary because we only need
r²= to find the area.
The area is
A = pr² = p() = 
which is approximately 31.66 square units.
Edwin
