Question

X^2 + y^2 +2x+6y=26

Answer 1

Complete the squares:

$(x {}^{2} + 2x + 1) - 1 = (x + 1) {}^{2} - 1$

$(y {}^{2} + 6y + 9) - 9 = (y + 3) {}^{2} - 9$

$(x + 1) {}^{2} - 1 + (y + 3) {}^{2} - 9 = 26$

$(x + 1) {}^{2} + (y + 3) {}^{2} = 26 + 10$

$(x + 1) {}^{2} + (y + 3) {}^{2} = 36$

General form:

$(x - a) {}^{2} + (y - b) {}^{2} = r {}^{2}$

Center coordinates:

I ( a , b )

I ( -1 , -3 )

Radius:

$r {}^{2} = 36$

$r = \sqrt{36} = 6$

Answer 2

Answer:

centre = (- 1, - 3 ) , radius = 6

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 + 2x + 6y = 26 ( collect x and y terms )

x² + 2x + y² + 6y = 26

using the method of completing the square

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

x² + 2(1)x + 1 + y² + 2(3)y + 9 = 26 + 1 + 9

(x + 1)² + (y + 3)² = 36 ← in standard form

with centre = (- 1, - 3 ) and r = $\sqrt{36}$ = 6