Find the circle and radius of circle at x^2 +y^2 +10x - 6y + 14=0

see explanation

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k ) are the coordinates of the centre and r is the radius

Given

x² + y² + 10x - 6y + 14 = 0 ( collect the x/ y terms together and subtract 14 from both sides )

x² + 10x + y² - 6y = - 14

Using the method of completing the square

add ( half the coefficient of the x/ y terms )² to both sides

x² + 2(5)x + 25 + y² + 2(- 3)y + 9 = - 14 + 25 + 9

(x + 5)² + (y - 3)² = 20 ← in standard form

with centre = (- 5, 3 ) and r = = 2