Answer:
The general equation of a circle is x² + y² - 6x - 16y + 48 = 0 .
Step-by-step explanation:
The standard form of equation of circle.
Where (h,k) is the centre of a circle and r is the radius.
As given
The center of a circle is located at (3, 8), and the circle has a radius that is 5 units .
Put in the formula
(By using the formula (a - b)² = a² + b²- 2ab)
As 5² = 25
x² + 9 - 6x + y² + 64 - 16y = 25
x² + y² - 6x - 16y + 9 + 64 = 25
x² + y² - 6x - 16y + 73 = 25
x² + y² - 6x - 16y + 73 - 25 = 0
x² + y² - 6x - 16y + 73 - 25 = 0
x² + y² - 6x - 16y + 48 = 0
(As the general equation of a circle are in the form x² + y² + Ax +By + F =0 Where A,B and C are constant .)
Therefore the general equation of a circle is x² + y² - 6x - 16y + 48 = 0 .