The equation x2 - 12x - 60 = -y2 - 4y describes a circle in the coordinate plane. find the radius of the circle and the coordina
1 answer:
Answer:
r = 10 , centre = (6, - 2 )
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 - 12x - 60 = - y² - 4y ( add y² + 4y to both sides )
x² - 12x + y² + 4y - 60 = 0 ( add 60 to both sides )
x² - 12x + y² + 4y = 60
using the method of completing the square
add ( half the coefficient of the x and y terms )² to both sides
x² + 2(- 6)x + 36 + y² + 2(2)y + 4 = 60 + 36 + 4
(x - 6)² + (y + 2)² = 100 ← in standard form
with centre = (6, - 2 ) and r = = 10
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