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

what is the center

what is the radius

please show calculations/steps

2 Answers

2 votes

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 = √(36) = 6

User Zabs
by
8.4k points
4 votes

Answer:

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

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 =
√(36) = 6

User Jmagin
by
8.7k points

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