Question

What is the center and radius of the circle given by x2 + y2 - 10x - 12y + 24 = 0?​

Answer 1

Answer:

centre (5, 6 ) , r = $\sqrt{37}$

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 the radius

given

x² + y² - 10x - 12y + 24 = 0 ( collect x and y terms together and subtract 24 from both sides )

x² - 10x + y² - 12y = - 24

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(- 6)y + 36 = - 24 + 25 + 36

(x - 5)² + (y - 6)² = 37 ← in standard form

with centre (h, k ) = (5, 6 ) and r = $\sqrt{37}$