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

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560047712The 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

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altavistardHint: 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)