The equation x2 y2 2x 6y 10 0 represents a circle Find

The equation x^2 + y^2 - 2x + 6y + 10 = 0 represents a circle. Find the center. Find the radius. Let f(x) = squareroot x + 4 and g(x) = x^2 + 3. Find (f g)(x). Find (g f)(x).

Solution

1) .given x^2 +y^2 -2x +6y +10=0

       we can rewrite the equation as

    x^2 -2x + y^2 +6y =10

now add and subtract 1

x^2 -2x +1 + y^2 +6y -1 =10

now x^2 -2x +1 can be wrriten as (x-1)^2

by the fromule (a-b)^2 =a^2 -2ab +b^2

so the equation becomes

(x-1)^2 +y^2 +6x -1 =10

now add and subtract 9

(x-1)^2 +y^2 +6x + 9 -9 -1 =10

(x-1)^2 +(y+3)^2 -10 =10

(x-1)^2 + (y+3)^2 =10+10

(x-1)^2 + (y+3)^2 =20

this is of the form

(x-a)^2 + (y-b)^2 = r^2

where (a,b) is the center and r=radius

so center (1,-3)

and r^2 = 20

     r = sqrt(20)

    r = 2 sqrt(5)

please ask second question again