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Select the center of the circle represented by the equation x^2+y^2-8x+11y-2=0

1 Answer

4 votes

Answer:

centre = (4, -
(11)/(2) )

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 - 8x + 11y - 2 = 0 ( collect terms in x and y together and add 2 to both sides )

x² - 8x + y² + 11y = 2

using the method of completing the square

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

x² + 2(- 4)x + 16 + y² + 2(
(11)/(2) )y +
(121)/(4) = 2 + 16 +
(121)/(4)

(x - 4)² + (y +
(11)/(2) )² =
(193)/(4) ← in standard form

with centre (4, -
(11)/(2) )

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