Standard form of equation of a circle:
(x - a)^2 + (y -b)^2 = r ^2.
Where centre = (a , b)
r = radius.
Centre (4 , -5) = (a , b) , a = 4, b = -5.
r = 5.5.
(x - 4)^2 + (y - -5)^2 = 5.5^2
(x - 4)^2 + (y +5)^2 = 5.5^2 Expand brackets, and use your calculator
x^2 - 8x + 16 + y^2 +10y + 25 = 30.25
x^2 - 8x + y^2 +10y + 25 +16 - 30.25 = 0
x^2 - 8x + y^2 +10y - 10.25 = 0.
x^2 + y^2 -8x +10y - 10.25 = 0. That's the equation of the circle.
or 10.25 = 10 /1/4 = 41/4
x^2 + y^2 -8x +10y - 41/4 = 0 Multiply both sides of the equation by 4.
4x^2 + 4y^2 -32x +40y - 41 = 0
Cheers.
