Write the equation of the circle with the given center and length of a radius

Question

Center at (3,5) and r=2
Thanks.

Answer 1

Circle equation is (x - h)^2 + (y - k)^2 = r^2

Center (h, k) = (3, 5) and r = 2

Substitute (h, k) = (3, 5) and r = 2 in (x  - h)^2 + (y - k)^2 = r^2

(x - 3)^2 + (y - 5)^2 = 2^2

x^2 - 6x  + 9 + y^2 - 10y  + 25 = 4

x^2 + y^2 - 6x - 10y  + 25 = 4

Subtract 4 from each side.

x^2 + y^2 - 6x - 10y  + 25 - 4 = 0

x^2 + y^2 - 6x - 10y  + 21 = 0.

Required circle equation is

x^2 + y^2 - 6x - 10y  + 21 = 0.

Answer 2

Circle equation is (x - h)^2 + (y - k)^2 = r^2

Center (h, k) = (3, 5) and r = 2

Substitute (h, k) = (3, 5) and r = 2 in (x  - h)^2 + (y - k)^2 = r^2

(x - 3)^2 + (y - 5)^2 = 2^2

x^2 - 6x  + 9 + y^2 - 10y  + 25 = 4

x^2 + y^2 - 6x - 10y  + 34 = 4

Subtract 4 from each side.

x^2 + y^2 - 6x - 10y  + 34 - 4 = 0

x^2 + y^2 - 6x - 10y  + 30 = 0.

Required circle equation is

x^2 + y^2 - 6x - 10y  + 30 = 0.