Answer:
A ≈ 154 units²
Explanation:
the area (A) of a circle is calculated as
A = πr² ( r is the radius)
to calculate the area we require to know r
the equation of a circle in standard form is
(x - h)² + (y - k)² = r²
given
x² + y² + 4x - 8y - 29 = 0
collect x and y terms together and add 29 to both sides )
x² + 4x + y² - 8y = 29
obtain standard form for circle using the method of completing the square
add ( half the coefficient of the x/ y terms)² to both sides
x² + 2(2)x + 4 + y² + 2(- 4)y + 16 = 29 + 4 + 16
(x + 2)² + (y - 4)² = 49 = r² ← in standard form
Then
A = πr² = π × 49 ≈ 154 units² ( to the nearest whole unit )