Mathematics
chungtony44
11

Rewrite 2x^2 + 2y^2 -8x +10y + 2 = 0 in standard form. Find the center and radius of the circle. Show all of your work for full credit.

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(1) Answers
andre84151

in form (x-h)^2+(y-k)^2=r^2 center is (h,k) and radius is r complete the squaer for everybody group x and y's sepereatley (2x^2-8x)+(2y^2+10y)+2=0 undistribute  the quadratic coefneints 2(x^2-4x)+2(y^2+5y)+2=0 take 1/2 of each linear coefient, squaer them then add negtive and positive inside psarenthaseses -4/2=-2, (-2)^2=4 5/2=2.5, 2.5^2=6.25 2(x^2-4x+4-4)+2(y^2+5y+6.25-6.25)+2=0 factor perfect squares 2((x-2)^2-4)+2((y+2.5)^2-6.25)+2=0 expand 2(x-2)^2-8+2(y+2.5)^2-12.5+2=0 2(x-2)^2+2(y+2.5)^2-18.5=0 add 18.5 to both sides 2(x-2)^2+2(y+2.5)^2=18.5 divide both sides by 2 (x-2)^2+(y+2.5)^2=9.25 (x-2)^2+(y-(-2.5))^2=(√9.25)^2 the center is (2,-2.5) and radius is √9.25

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