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Question 36700: write the equation of the given circles in standard form:
1) x^2+y^2-6x+8y+9=0
2) 2x^2+2y^2-4x-28y+66=0
Answer by venugopalramana(3286)   (Show Source):
You can put this solution on YOUR website! write the equation of the given circles in standard form:
1) x^2+y^2-6x+8y+9=0
COMPLETE SQUARE
(X^2-2X*3+3^2)-3^2+(Y^2+2Y*4+4^2)-4^2+9=0
(X-3)^2+(Y+4)^2=9+16-9=16=4^2
THIS IS IN THE STANDARD FORM
(X-H)^2+(Y-K)^2=R^2.....WHERE (H,K)IS THE CENTRE AND R IS THE RADIUS OF THE CIRCLE
2) 2x^2+2y^2-4x-28y+66=0..DIVIDE BY 2 AND COMPLETE SQUARE
(X^2-2X*1+1^2)-1^2+(Y^2-2Y*7+7^2)-7^2+33=0
(X-1)^2+(Y-7)^2=1+49-33=17={SQRT(17)}^2
THIS IS IN THE STANDARD FORM
(X-H)^2+(Y-K)^2=R^2.....WHERE (H,K)IS THE CENTRE AND R IS THE RADIUS OF THE CIRCLE
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