Question

X^2+8x+y^2-4y=5 find the radius and the center point of the circle

Answer 1

centre = (- 4, 2 ) , radius = 5

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

x² + 8x + y² - 4y = 5

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(- 2)y + 4 = 5 + 16 + 4

(x + 4)² + (y - 2)² = 25 ← in standard form

with (h, k ) = (- 4, 2 ) and r =
`√(25)` = 5

centre = (- 4, 2 ) and radius = 5