Question

For each of the following equations,give the centre and radius of the circle.

a)x^2 + y^2 = 25 b) x^2 + y^2= 1
d) (x - 5)^2 + (y-3)^2 = 81 e) (x+2)^2 + (y-1)^2 = 9
g) (x + 1)^2 + (y + 3)^2 = 49 h) x^2+ y^2 = 6.25

Answer 1

a) Center is (0,0) and radius r = 5

b) Center is (0,0) and radius r = 1

d) Center is (5,3) and radius r = 9

e Center is (-2,1) and radius r = 3

g) Center is (-1,-3) and radius r = 7

h) Center is (0,0) and radius r = 2.5

Explanation:

a)

Given circle x² + y² = 25

The standard form of circle equation is

( x-h)² +(y-0)² = r²

Center is (0,0) and radius r = 5

b)

Given circle x² + y² = 1

The standard form of circle equation is

( x-h)² +(y-0)² = r²

Center is (0,0) and radius r = 1

d)

Given circle (x-5)² + (y-3)² = 81

The standard form of circle equation is

( x-h)² +(y-0)² = r²

(x-5)² + (y-3)² = 9²

Center is (5,3) and radius r = 9

e)

Given circle (x+2)² + (y+1)² = 9

The standard form of circle equation is

( x-h)² +(y-0)² = r²

(x+2)² + (y+1)² = 3²

Center is (-2,-1) and radius r = 3

g)

Given circle (x+1)² + (y+3)² = 49

The standard form of circle equation is

( x-h)² +(y-0)² = r²

(x+1)² + (y+3)² = 7²

Center is (-1,-3) and radius r = 7

h)

Given circle x² + y² = 6.25

The standard form of circle equation is

( x-h)² +(y-0)² = r²

Given circle x² + y² = (2.5)²

Center is (0,0) and radius r = 2.5