A circle has the equation x2 + y2 - x + 10y + 13 = 0. What is the radius of this circle?

The radius would be 4. Move all variables to the left side and all constants to the right side. x2 + y2 - 4x-10y=-13+0 x2 + y2 - 4x-10y=-13+0 Add - 13 - 13 and 00 to get - 13 - 13. x2 + y2 - 4x-10y=-13 x2 + y2 - 4x-10y=-13 Complete the square for x2 - 4x x2 - 4x. Tap for more steps ... (x-2) 2 - 4 (x-2) 2 - 4 Substitute (x-2) 2 - 4 (x-2) 2 - 4 for x2 - 4x x2 - 4x in the equation x2 + y2 - 4x-10y=-13 x2 + y2 - 4x-10y=-13. (x-2) 2 - 4 + y2 - 10y=-13 (x-2) 2 - 4 + y2 - 10y=-13 Move - 4 - 4 to the right side of the equation by adding 44 to both sides. (x-2) 2 + y2 - 10y=-13+4 (x-2) 2 + y2 - 10y=-13+4 Complete the square for y2 - 10y y2 - 10y. Tap for more steps ... (y-5) 2 - 25 (y-5) 2 - 25 Substitute (y-5) 2 - 25 (y-5) 2 - 25 for y2 - 10y y2 - 10y in the equation x2 + y2 - 4x-10y=-13 x2 + y2 - 4x-10y=-13. (x-2) 2 + (y-5) 2 - 25=-13+4 (x-2) 2 + (y-5) 2 - 25=-13+4 Move - 25 - 25 to the right side of the equation by adding 2525 to both sides. (x-2) 2 (y-5) 2 = - 13+4+25 (x-2) 2 (y-5) 2 = - 13+4+25 Add - 13 - 13 and 44 to get - 9 - 9. (x-2) 2 + (y-5) 2 = - 9+25 (x-2) 2 + (y-5) 2 = - 9+25 Add - 9 - 9 and 2525 to get 1616. (x-2) 2 + (y-5) 2 = 16 (x-2) 2 + (y-5) 2 = 16 This is the form of a circle. Use this form to determine the center and radius of the circle. (x-h) 2 + (y-k) 2 = r2

r=4 r=4 h=2 h=2 k = 5

Hint: Make your " x2 + y2 - x + 10y + 13 = 0" clearer by using " ^ " to indicate exponentiation:

x^2 + y^2 - x + 10y + 13 = 0

Rearrange this so that x terms are together and y terms are also (separately):

x^2 - 1x + y^2 + 10y + 13 = 0

Complete the square twice: once for x and once for y:

(x^2 - 1x + (-1/2) ^2 - (-1/2) ^2 + y^2 + 10y + 25 - 25 = - 13

Condense:

(x-1/2) ^2 + (y+5) ^2 - 1/4 - 25 = - 13

Combine - 1/4, - 25 and - 13:

(x-1/2) ^2 + (y+5) ^2 - 1/4 - 25 = - 13 + 1/4 + 25 = 11 3/4 = 47/4

Then we have (x-1/2) ^2 + (y+5) ^2 = 47/4, and r^2 = 47/4. Then the radius of the circle is sqrt (47/4) = sqrt (47) / 2 (answer)